# Contribution List

Showing 247 of 247 submitted abstracts

###### Gabriel Verret, The University of Western Australia
Over the past few years, there has been an explosion of results classifying arc-transitive (or $2$-arc-transitive, arc-regular, etc...) graphs of valency $d$ and order $kp^n$, where $d,k,n$ are fixed integers and $p$ is a prime that is allowed to vary. These results are often proved by standard methods and thus t... More
###### Dr. Yusuke Suzuki, Niigata University
We discuss the existence of minors of given graphs in optimal $1$-planar graphs. As our first main result, we prove that for any graph $H$, there exists an optimal $1$-planar graph which contains $H$ as a topological minor. Next, we consider minors of complete graphs, and prove that every optimal $1$-planar graph ... More
###### Mr. Martin Knor, Slovak University of Technology in Bratislava
Wiener index, the sum of all distances in a graph, is probably the most important topological descriptor. There are several papers establishing congruence relations for the Wiener index in various classes of graphs. We generalized the results of Lin and we obtained congruence relations for large families of graphs w... More
###### Prof. Marco Buratti, Università di Perugia
Let $V$ be the set of vertices of a regular polygon in the plane and let $L(V)$ be the set of all lengths of all open polygonal curves with vertex-set $V$. Which is the size of $L(V)$? I conjecture that if $|V|=2n+1$ is a prime, then the answer is ${3n-1\choose n-1}$. I will show that this conjecture is equivalent t... More
Product graphs and product-like structures play a central role in theoretical biology. To determine traits that can vary independently through evolution one can equivalently ask for the (local) prime factors of the underlying phenotypespace. The topology of the phenotypespace corresponds (at least locally) to the di... More
###### Prof. Daniel Marques Pinto, University of Coimbra
If we take three perfect binary trees of the same height we can build a trivalent graph, that we will call \emph{quasi-binary tree}, by adding an edge from each one of the three root vertices of the original trees to a new vertex. We will show that, for all $n \in \mathbb{N}$, there is a way of gluing three quasi-b... More
###### Dr. Rastislav Krivoš-Belluš, P. J. Šafárik University in Košice
$k$-Path Vertex Cover Problem is NP-hard for several classes of graphs. We have focused on the weighted version of this problem. We will analyze complexity of exact algorithms for finding minimum $k$-Path Vertex Cover for trees and cacti graphs using dynamic programming and with parametrized complexity depending on ... More
###### Dr. Nicolas Lichiardopol, Lycée Craponne, Salon
An oriented graph $D$ is said to be traceable if it admits a hamiltonian path. For $k\geq 2$, an oriented graph $D$ of order at least $k$, is said to be $k$-traceable if any subset of $k$ vertices of $D$ induces a traceable oriented graph. We denote by $t(k)$ the smallest integer bigger than or equal to $k$ such th... More
###### Prof. Jianfeng Wang, Qinghai Normal University
In this report, we will introduce a new lower bound for the first Zagreb index and determine all the extreme graphs. These results not only contain many previous ones but are helpful to find new graphs determined by the Laplcian spectra. More
###### Prof. Martyn Mulder, Econometrisch Instituut, Erasmus Universiteit
In social choice theory the process of achieving consensus can be modeled by a function $L$ on the set of all finite sequences of vertices of a graph. It returns a nonempty subset of vertices. To guarantee rationality of the process {\em consensus axioms} are imposed on $L$. Three such axioms are Anonymity, Betweenn... More
###### Mr. Christoph Brause, TU Bergakademie Freiberg
The Maximum Independent Set Problem (MISP for short) and the Minimum $k$-Path Vertex Cover Problem (M$k$PVCP for short) are known to be NP-hard [2,1]. For the first problem, there exists lots of graph classes in terms of forbidden subgraphs, where polynomial algorithms compute optimal solutions. A celebrated result ... More
###### Dr. Aleksandra Tepeh, FEECS, University of Maribor and FIŠ, Novo mesto
The Wiener index $W(G)$ of a connected graph $G$ is defined to be the sum $\sum_{u,v} d(u,v)$ of distances between all unordered pairs of vertices in $G$. Similarly, the edge-Wiener index $W_e(G)$ of $G$ is defined to be the sum $\sum_{e,f} d(e,f)$ of distances between all unordered pairs of edges in $G$, or equ... More
###### Iztok Peterin, FEECS, University of Maribor and IMFM Ljubljana
In [Discrete Math. 307 (2007) 472--483] a linear algorithm for the prime factor decomposition of a graph with respect to Cartesian product is presented. Hence the paper establishes the best possible complexity for this important fundamental problem. Unfortunately this algorithm has a big constant and its linearity b... More
###### Dr. Izolda Gorgol, Lublin University of Technology
A subgraph of an edge-coloured graph is {\it rainbow} if all of its edges have different colours. For graphs $G$ and $H$ the {\it anti-Ramsey number} $ar(G,H)$ is the maximum number of colours in an edge-colouring of $G$ with no rainbow copy of $H$. The notion was introduced by Erd\H os, Simonovits and V.~S\'os and... More
###### Kenneth Walter Johnson, Penn State University
Given any finite quasigroup $Q$ an association scheme can be automatically constructed from the "class algebra". Moreover if $Q$ is a loop (i.e there is an identity element) the association scheme may be regarded as an S-ring over $Q$ (with suitable modifications to the definition). Recently Humphries and I have... More
###### Dr. Sho Suda, Aichi University of Education
Hadamard matrices have been widely studied from the view point of design theory, coding theory, quantum information theory. Algebraic combinatorics also contributes the study for Hadamard matrices. For example, it was shown that Hadamard matrices have a structure of a distance regular graph of diameter 4. In this ta... More
###### Mr. Uffe Thorsen, IMADA, University of Southern Denmark
By modeling molecules as graphs it is possible to infer atom to atom mappings of chemical reactions by solving the minimum edge edit distance problem. This can among other things be used to generate graph grammar rules for use in generative chemistry. Another application is to complete chemical or biological network... More
###### Mr. Richard Hammack, Virginia Commonwealth University
We are concerned with automorphism groups of thin direct products. (A graph is {\it thin} if no two vertices have the same neighborhood.) It is known that if $\varphi$ is an automorphism of a connected non-bipartite thin graph $G$ that factors (uniquely) into primes as $G=G_1\times G_2\times\cdots\times G_k$, t... More
###### Prof. Halina Maria Bielak, Inst. of Math., UMCS, Lublin
Let $\mathcal{H}=(V,\mathcal{E})$ be a simple linear hypergraph. We consider a blow-up hypergraph $\mathcal{G}[\mathcal{H}]$ of $\mathcal{H}$. We are interested in the following problem. We have to decide whether there exists a blow-up hypergraph $\mathcal{B}[\mathcal{H}]$ of $\mathcal{H}$, with given hypere... More
###### Dr. Pablo Spiga, University of Milano-Bicocca
The celebrated Erdos-Ko-Rado theorem determines the cardinality and also describes the structure of a set of maximal size of intersecting k-subsets from a set of size n. Analogous results hold for many other combinatorial objects and in this talk we are concerned with a weak extension of the Erdos-Ko-Rado theorem to... More
###### Mr. Thomas Perrett, Technical University of Denmark
The \emph{chromatic polynomial} $P(G,t)$ of a graph $G$ is a polynomial with integer coefficients which counts, for each non-negative integer $t$, the number of proper $t$-colourings of $G$. A real number $t$ is called a \emph{chromatic root} of $G$ if $P(G,t) = 0$. An interval $I\subseteq \mathbb{R}$ is called \emp... More
###### Dr. Binod Kumar Sahoo, National Institute of Science Education and Research, Bhubaneswar
Let $q$ be a prime power and $W(q)$ be the symplectic generalized quadrangle of order $q$. For $q$ even, let $\mathcal{O}$ (respectively, $\mathcal{E}$, $\mathcal{T}$) be the binary linear code spanned by the ovoids (respectively, elliptic ovoids, Tits ovoids) of $W(q)$ and $\Gamma$ be the graph defined on the set ... More
###### Prof. Fuji Zhang, Xiamen University
In this paper, we find all binary Hamming tilings (i.e. the tilings corresponding to binary Hamming graphs) in Archimedean tilings and show the only four such tilings are (4; 4; 4; 4),(6; 6; 6),(4; 8; 8) and (4; 6; 12). Then we compute the Wiener number of some plane connected subgraphs of binary Hamming tili... More
###### Dr. Stefko Miklavic, University of Primorska
Let $\Gamma$ denote a bipartite distance-regular graph with diameter $D \ge 4$ and valency $k \ge 3$. Let $X$ denote the vertex set of $\Gamma$. Fix $x \in X$ and let $T=T(x)$ denote the corresponding Terwilliger algebra of $\Gamma$. In this talk we consider the situation where, up to isomorphism, $\Gamma$ has exa... More
###### Dr. Kenta Ozeki, National Institute of Informatics
A {\em book embedding\/} of a graph $G$ is to put the vertices along the {\em spine\/} (a segment) and each edge of $G$ on a single {\em page\/} (a half-plane with the spine as its boundary) so that no two edges intersect transversely in the same page. We say that a graph $G$ is {\em $k$-page embeddable\/} if $G$ h... More
###### Dr. Michael Giudici, The University of Western Australia
Given a finite graph $\Gamma$ with $n$ vertices, can we obtain useful bounds on the number of automorphisms of $\Gamma$? If $\Gamma$ is vertex transitive then $|\mathrm{Aut}(\Gamma)|=n|G_v|$ and so the question becomes one about $|G_v|$. When $\Gamma$ is a cubic arc-transitive graph then Tutte showed that $|G_v|$ di... More
###### Mr. Alexander Mednykh, Sobolev Institute of Mathematics
In this lecture we give a short survey of old and new results about branched coverings of graphs. This notion was introduced independently by T.~D. Parsons, T.~Pisanski, P.~Jackson (1980), H.~Urakawa (2000), B.~Baker, S.~Norine (2009) and others. The branched covering of graphs are also known as harmonic maps or v... More
###### Dr. Kieka Mynhardt, University of Victoria
A \emph{broadcast} on a nontrivial connected graph $G=(V,E)$ is a function $f:V\rightarrow\{0,1,\dots,$ $\operatorname{diam}G\}$ such that $f(v)\leq e(v)$ (the eccentricity of $v$) for all $v\in V$. The \emph{cost} of $f$ is $\sigma(f)=\sum_{v\in V}f(v)$. A broadcast $f$ is a \emph{dominating broadcast }if every... More
###### Dr. Allen Herman, University of Regina
Given two finite association schemes $(X,T)$ and $(X,S)$ of the same order, we say that $T$ is a fusion of $S$ if every relation in $T$ is a union of relations in $S$. This talk will discuss two computer algorithms for detecting the fusions of a given association scheme. The first directly calculates fusions of... More
###### Prof. Jonathan L. Gross, Columbia University
In calculations of genus polynomials for a recursively specifiable sequence of graphs, the imbeddings of each of the graphs are partitioned into \textit{imbedding-types}. The effects of a recursively applied graph operation $\tau$ on each imbedding-type are represented by a \textit{production matrix}. We demonstra... More
###### Mr. Niko Tratnik, FNM UM
Carbon nanotubes are chemical compounds made of carbon which possess a cylindrical structure. Open-ended single-walled carbon nanotubes are called tubulenes. The resonance graph of a tubulene reflects the interference among its Kekul\'e structures. First we will present some basic properties of tubulenes and their ... More
###### Mr. Connor Thomas, Université libre de Bruxelles
C-groups are smooth quotients of Coxeter groups. It is well known that there is a one-to-one correspondence between string C-groups and abstract regular polytopes. Recently, some results were obtained in the more general case of C-groups without any condition on the diagram. I will present the classification o... More
###### Mr. Jeremie Moerenhout, University of Auckland
We discuss the existence of chiral polyhedra with automorphism group isomorphic to an almost simple groups with socle $PSL(2,q)$. We prove that there exists such a chiral polyhedron if and only if its group is not $M(1,9)$, $PSL(2,q)$ or $PGL(2,q)$ for any prime power $q$. More
###### Prof. Ingo Schiermeyer, Technische Universität Bergakademie Freiberg
In this talk we study the chromatic number of $P_5$-free graphs. Gy\'arfas has shown \medskip \noindent{\bf{Theorem}} Let $G$ be a $P_k$-free graph for $k \geq 4$ with clique number $\omega(G) \geq 2.$ Then $\chi(G) \leq (k-1)^{\omega(G)-1}.$ \medskip and has posed the following question: \medskip ... More
###### Mr. Tilen Marc, IMFM
Partial cubes are graphs isometrically embeddable into hypercubes. In the talk I will present a complete classification of cubic, vertex-transitive partial cubes. Results can be seen as a generalization of results of Bre\v sar et. al. from 2004 on cubic mirror graphs, and a contribution to the classification of all ... More
###### Mr. Veerapas Boonthong, Chulalongkorn University
The distance multigraph of a graph $G$ is the multigraph having the same vertex set as $G$ with $d_G(u, v)$ edges connecting each pair of vertices $u$ and $v$, where $d_G(u, v)$ is the distance between vertices $u$ and $v$ in a graph $G$. This work gives a technique to find a clique decomposition of the distance mul... More
###### Prof. Peter F. Stadler, University Leipzig
Phylogenomics heavily relies on well-curated sequence data sets that consist, for each gene, exclusively of 1:1-orthologs, i.e., of genes that have arisen through speciation events. Paralogs, which arose from duplication events, are treated as a dangerous nuisance that has to be detected and removed. Building upon ... More
###### Mr. Martin Merker, Technical University of Denmark
The Tree Decomposition Conjecture by B\'arat and Thomassen states that for every tree $T$ there exists a natural number $k(T)$ such that the following holds: If $G$ is a $k(T)$-edge-connected graph with size divisible by the size of $T$, then $G$ can be edge-decomposed into subgraphs isomorphic to $T$. So far this c... More
###### Dr. Christoph Flamm, University of Vienna
Various measures e.g. atom economy or number of used reactions are frequently used in Organic Synthesis to evaluate and compare different total synthesis'. These measures shape the strategies how organic chemists design a synthesis to a target molecule. Metabolic engineering, a sub-field of Synthetic Biology, inve... More
###### Dr. Debra Boutin, Hamilton College
A {\it determining set} $S$ is a set of vertices with the property that each automorphism of the graph is uniquely identified by its action on $S$. The {\it distinguishing number} is the smallest number of colors necessary to color the vertices so that no nontrivial automorphism preserves the color classes. If a g... More
###### Dr. Atsuhiro Nakamoto, Yokohama National University
Wagner proved that any two plane {\em triangulations} with $n > 3$ vertices can be transformed into each other by diagonal flips. His proof gives us an algorithm to transform them by $O(n^2)$ diagonal flips. However, Komuro has given an algorithm with $O(n)$ diagonal flips, and proved that the order is best possib... More
###### Prof. Edwin van Dam, Tilburg University
A directed graph is called strongly $\ell$-walk regular if the number of walks of length $\ell$ from one vertex to another depends only on whether the two vertices are the same, adjacent, or not adjacent. This generalizes the concept of directed strongly regular graphs and a problem introduced by Hoffman. It also ge... More
###### Gábor Somlai, Ben Gurion University of Negev
The investigation of CI-groups started with the conjecture of \'Ad\'am. Using the terminology later introduced by Babai, he conjectured that every cyclic group is a CI-group. A group $G$ is called a CI-group when two Cayley graphs of $G$ are isomorphic only if there is an automorphism of the group $G$ which indu... More
###### Mr. Antonio González, University of Seville
In this talk, we discuss several relationships among some special sets of vertices of graphs such as metric-locating-dominating sets, locating-dominating sets and doubly resolving sets. First, we extend a result of Henning and Oellermann (2004) by proving that the location-domination number of a graph is... More
###### Prof. Kirsti Wash, Trinity College
Given two disjoint copies of a graph $G$, denoted $G^1$ and $G^2$, and a permutation $\pi$ of $V(G)$, the graph $\pi G$ is constructed by joining $u \in V(G^1)$ to $\pi(u) \in V(G^2)$ for all $u \in V(G^1)$. $G$ is said to be a universal fixer if the domination number of $\pi G$ is equal to the domination number of ... More
###### Mr. Cherif Sellal, Polytechnique de Montréal
We study necessary and sufficient conditions for existence of a simple graph $G$, and for a simple and connected graph $G'$ with given numbers $m_{ij}$ of edges with end-degrees $i$, $j$ for $i \le j \in \{1, 2, . . . , \Delta \}$ where $\Delta$ denotes the maximum degree of $G$ or $G'$. Applications in Mathemati... More
###### Dr. Hanna Furmanczyk, University of Gdansk
The minimum number of total independent sets of $V \cup E$ of graph $G(V,E)$ is called the \emph{total chromatic number} of $G$, denoted by $\chi''(G)$. If difference of cardinalities of any two total independent sets is at most one, then the minimum number of total independent partition sets of $V \cup E$ is calle... More
###### Dr. Petra Žigert Pleteršek, UM FKKT, UM FNM
Benzenoid systems or hexagonal systems are subgraphs of a hexagonal lattice. Open-ended carbon nanotubes alias tubulenes can be seen as an embedding of a benzenoid system to a surface of a cylinder with some perimeter edges being joined. Carbon nanotubes are interesting materials with some unusual properties and ... More
###### Dr. Domenico Labbate, Dipartimento di Matematica, Informatica ed Economia - Università degli Studi della Basilicata - Potenza
A graph $G$ is $1$--extendable if every edge belongs to at least one $1$--factor. %An orientation of a graph $G$ is an assignment of a {\em direction} to each %edge of $G$. Now suppose that Let $G$ be a graph with a $1$--factor $F$. Then an {\em even $F$--orientation} of $G$ is an orientation in which each $F$-... More
###### Prof. Stanislav Jendroľ, P. J. Šafárik University in Košice
Let $G=(V,E,F)$ be a connected loopless and bridgeless plane graph, with vertex set $V$, edge set $E$, and face set $F$. Let $X\in\{V,E,F,V\cup E,V\cup F,E\cup F,V\cup E\cup F\}$: Two elements $x$ and $y$ of $X$ are \emph{facially adjacent} in $G$ if they are incident, or they are adjacent vertices, or adjacent face... More
###### Mr. Mate Vizer, MTA Alfréd Rényi Institute of Mathematics
Suppose we are given a set of $n$ balls $\{b_1,\ldots,b_n\}$ each colored either red or blue in some way unknown to us. To find out some information about the colors, we can query any triple of balls $\{b_{i_1},b_{i_2},b_{i_3}\}$. As an answer to such a query we obtain (the index of) a {\em majority ball}, that is... More
###### Mr. Pierre Hansen, HEC Montréal
Computers have been used extensively to solve exactly or approximately a large variety of combinatorial otimization problems defined on graphs. It has also been noticed, in the last two decades, that computers can be used to advance graph theory {\it per se}. Several systems (e.g., Graph, Graffiti, AutoGraphiX, Grap... More
###### Prof. Liming Xiong, Beijing Insititute of Technology
In this talk, we present some results relation between forbidden subgraphs and hamiltonian propertices (such as the existence of hamiltonian cycles, hamiltonian paths and spanning closed trails et.al). In particular, our results show how it affects the forbidden subgraphs to guarteeing the same hamiltonian propertic... More
###### Dr. Valentina Pepe, Sapienza University of Rome
Let $H$ be a fixed graph. The {\em Tur\'an number} of $H$, denoted $ex(n,H)$, is the maximum number of edges that a graph with $n$ vertices and not containing a copy of $H$ can have. When $H$ is bipartite, in many cases, even the question of determining the right order of magnitude for $ex(n,H)$ is not known. We hav... More
###### Mr. Mou Gao, Nanyang Technological University
We show that every $\frac{1}{k-1}$-tough $2K_2$-free graph admits a $k$-walk, and it can be found in polynomial time. For this class of graphs, this proves a long-standing conjecture due to Jackson and Wormald (1990). Furthermore, we prove that every $(1+\epsilon)$-tough $2K_2$-free graph is prism-Hamiltonian. ... More
###### Dr. Ismael Gonzalez Yero, University of Cadiz
Graph structures may be used to model computer networks. Each vertex in a graph is a possible location for an intruder (fault in a computer network, spoiled device). So, a correct surveillance of each vertex of the graph to control such a possible intruder would be worthwhile. In this sense, Slater (1975) brought in... More
###### Mr. Barry Monson, University of New Brunswick
If you truncate an equilateral triangle $\{3\}$ to its edge midpoints you get another, smaller $\{3\}$. If you truncate a regular tetrahedron $\{3, 3\}$ to its edge midpoints, you get (a little unexpectedly) a regular octahedron $\{3, 4\}$. In higher ranks, the fully truncated n-simplex $\mathcal{T}_n$ is no ... More
###### Mr. Simon Schmidt, Joseph Fourier's University Grenoble
The domination game is played on a graph $G$ by Dominator and Staller. The two players are taking turns choosing a vertex from $G$ such that at least one previously undominated vertex becomes dominated. Dominator wants to finish the game as fast as possible, while Staller wants to prolong it. The game is called D-ga... More
###### Prof. Emrah Akyar, Anadolu University
In this study we consider a graph coloring game invented by Bodlaender and Brams independently. Let $G=(V,E)$ be a finite simple graph and $X$ be a set of colors. The game chromatic number of $G$ is defined via a two-person finite game. Two players, generally called Alice and Bob, with Alice going first, alternative... More
###### Mr. Jesus Leanos Macias, University of Maribor
Gauss has given necessary but not sufficient conditions for a sequence of letters to represent the sequence of self-crossings of some closed planar curve. Such sequences of letters were called Gaussian words and recently generalized to Gaussian paragraphs, sets of words that arise from sequences of crossings of seve... More
###### Dr. Gábor Nyul, Institute of Mathematics, University of Debrecen
B. Duncan and R. Peele were the first who studied enumeration of independent partitions of graphs from a combinatorial point of view, and introduced Stirling numbers of the second kind and Bell numbers for graphs. In our talk, we present properties of these numbers and values for special graphs, as well as their ... More
###### Dr. Tetsuji Taniguchi, Hiroshima Institute of Technology
Hoffman graphs were introduced by Woo and Neumaier [2] to extend the results of Hoffman [1]. Hoffman proved what we would call Hoffman's limit theorem which asserts that, in the language of Hoffman graphs, the smallest eigenvalue of a fat Hoffman graph is a limit of the smallest eigenvalues of a sequence of ... More
###### Prof. Xian'an Jin, Xiamen University
In this talk, we first give a relation between the Homfly polynomal and the weighted Tutte polynomial. Then we discuss applications of the relation to DNA double crossover polyhedra. More
###### Mr. Gábor Tardos, Rényi Institute, Budapest
Homomorphism duality pairs play a crucial role in the theory of relational structures and in the Constraint Satisfaction Problem. In this talk we concentrate on infinite-finite duality pairs of directed graphs. We find a characterization of infinite antichains that allow for a finite dual. The characterization rese... More
###### Dr. Paul Dorbec, Univ. Bordeaux - CNRS
In the domination game, two players alternate turns marking a vertex in a graph. When it is marked, a vertex must dominate at least one new vertex, either itself or one of its neighbours. When the set of marked vertices forms a dominating set (not necessarily minimal), the game comes to an end and the score of the g... More
###### Prof. Paul-Hermann Zieschang, Department of Mathematics, University of Texas, Brownsville, TX 78520
Let $S$ be a set, and let $\mu$ be a map from $S\times S$ to the power set of $S$. For any two elements $p$ and $q$ of $S$, we write $pq$ instead of $\mu(p,q)$ and assume that $pq$ is not empty. For any two non-empty subsets $P$ and $Q$ of $S$, we define the {\em complex product}\index{complex product} $PQ$ to be th... More
###### Dr. Dimitri Leemans, University of Auckland
In this talk we will show that all hypertopes whose automorphism group is a Suzuki simple group are necessarily hyperpolyhedra. We will also discuss future research directions in the same vein. More
###### Mr. Thomas William Tucker, Colgate University
e genus polynomial $g_G(z)=\Sigma a_iz^i$ of graph $G$ is the generating function where $a_i$ is the number of imbeddings of $G$ in the surface of genus $i$. A genus polynomial is always {\em interpolating}, that is the nonzero coefficients form an interval. Little else is known; for example the number of imbeddin... More
###### Prof. Xueliang Li, Center for Combinatorics, Nankai University
In this talk we will give a unified viewpoint on indices, polynomials and matrices of graphs. Starting from a graph with weights on edges or vertices, one can get various kinds of graph indices, graph polynomials, and graph matrices. Then, we can see that a lot of new and interesting objects can be taken into accoun... More
###### Prof. Rögnvaldur G. Möller, University of Iceland
Tutte's two papers from 1947 and 1959 on cubic graphs were the starting point of the in-depth study of the interplay between the structure of a group and the structure of a graph that the group acts on. In this talk I will describe applications of Tutte's ideas where it is assumed that the graph is infinite and the... More
###### Dr. Simon Mark Smith, City University of New York
We say that two permutation groups $A, B$ on the same set $X$ are {\em strongly orbit equivalent} if $A$ and $B$ have the same orbits on the power set $2^X$. Groups strongly orbit equivalent to finite symmetric groups were first considered by J. von Neumann and O. Morgenstern in 1947. We call a group $B$ {\em str... More
###### Dr. János Ruff, University of Pécs
A permutation of the affine space $AG(n,q)$ is called an integral automorphism if it preserves the integral distance defined among the points. The integral automorphisms which are also semiaffine transformations were determined by Kurz and Meyer (2009). In this talk, we show that there is no additional integral au... More
###### Mr. Hrant Khachatrian, Yerevan State University
An edge-coloring of a graph $G$ with colors $1,\ldots,t$ is an interval $t$-coloring if all colors are used, and the colors of edges incident to each vertex of $G$ are distinct and form an interval of integers. A graph $G$ is interval colorable if it has an interval $t$-coloring for some positive integer $t$. Fo... More
###### Dr. Susana Clara López, Universitat Politècnica de Catalunya
For $m\le n$, we denote the set $\{m,m+1,\ldots, n\}$ by $[m,n]$. Let $d$ be a positive integer. A {\it Langford sequence} of order $m$ and defect $d$ is a sequence $(l_1,l_2,\ldots, l_{2m})$ of $2m$ numbers such that (i) for every $k\in [d,d+m-1]$ there exist exactly two subscripts $i,j\in [1,2m]$ with $l_i=l_j=k$... More
###### Mr. Jozef Siran, Open University and Slovak University of Technology
It has been known that for diameters $k\in \{2,3,5\}$, graphs of diameter $k$ and maximum degree $q+1$ for infinite sets of prime powers $q$ and with orders asymptotically approaching the corresponding Moore bounds can be obtained from generalised triangles, quadrangles and hexagons. These graphs, however, are not v... More
###### Dr. Hiroshi Nozaki, Aichi University of Education
It is known that for any given integer $k\geq 3$ and real number $\lambda<2\sqrt{k-1}$, there are only finitely many $k$-regular graphs whose second largest eigenvalue is at most $\lambda$. In this talk, we give a new upper bound for the order of such a graph for given $k$ and $\lambda$. The main tool is the linear ... More
###### Prof. Gabor Korchmaros, Department of Mathematics, Informatics and Economy of University of Basilicata
We deal with some problems in Finite geometry arising from current research on $AG$ (algebraic-geometry) codes defined over the Hermitian curve. In $PG(2,q^2)$, let $\mathcal H$ be the Hermitian curve. For a fixed positive integer $d$, let $\mathbf{S}_d$ be the family of all degree $d$ plane algebraic curve... More
###### Prof. Paul Horn, University of Denver
Harnack inequalities relate the maximum and minimum values of eigenfunctions or positive solutions to the heat equation. These are classical in the manifold setting, and versions are also known for functions on graphs. It is known that a graph satisfying a so-called parabolic Harnack inequality is equivalent to the... More
###### Mr. Jakub Przybyło, AGH University of Science and Technology
It is well known that there are no \emph{irregular graphs}, understood as simple graphs with pairwise distinct vertex degrees, except the trivial $1$-vertex case. A graph invariant called the \emph{irregularity strength} was thus introduced aiming at capturing a level of irregularity of a graph. Suppose that given a... More
###### Dr. Marietjie Frick, University of South Africa
We say a graph $G$ has a property ${\cal P}$ \emph{locally} (or $G$ is \emph{locally} $\cal P$) if for every vertex $v$ in $G$, the graph induced by the open neighbourhood $N(v)$ of $G$ has property $\cal P$. For example, a graph $G$ is \emph{locally connected} if $G[N(v)]$ is connected for every vertex $v$ in $G$. ... More
###### Dr. Florent Foucaud, Université Blaise Pascal, Clermont-Ferrand
A locating-dominating set of a graph is a dominating set such that each vertex not in the set has a unique neighbourhood within the set. In 2014, Garijo, Gonz\'alez and M\'arquez conjectured that any twin-free graph without isolated vertices admits a locating-dominating set of size at most half the order. We discus... More
###### Ms. He Chen, Department of Mathematics, Southeast University
Let $G$ be an edge-colored graph. A rainbow (heterochromatic, or multicolored) path of $G$ is such a path in which no two edges have the same color. Let the color degree of a vertex $v$ to be the number of different colors that are used on edges incident to $v$, and denote it to be $d^c(v)$. It was showed that i... More
###### Mr. Riste Škrekovski, FMF, FIS, IMFM, FAMNIT
The Wiener index (i.e., the total distance or the transmission number), defined as the sum of distances between all unordered pairs of vertices in a graph, is one of the most popular molecular descriptors. In this talk, I will summarize some results, conjectures, and problems on this molecular descriptor, with emph... More
###### Prof. Irene Sciriha, University of Malta
A graph $G$ is singular of nullity $\eta$ if the nullspace of its adjacency matrix ${\bf G}$ has dimension $\eta$. Such a graph contains $\eta$ cores determined by a basis, with minimum support sum, for the nullspace of ${\bf G}$. These are induced subgraphs of singular configurations, the latter occurrin... More
###### Andrej Taranenko, Faculty of Natural Sciences and Mathematics, University of Maribor
We introduce an apparatus to measure closeness or relationship of two given objects. This is a topology based apparatus that uses graph representations of the compared objects. In more detail, we obtain a metric on the class of all pairwise non-isomorphic connected simple graphs to measure closeness of two such gra... More
###### Dr. Robert Bailey, Grenfell Campus, Memorial University
The metric dimension of a graph $\Gamma$ is the least size of a set of vertices $\{v_1, \ldots, v_m\}$ with the property that, for any vertex $w$, the list of distances from $w$ to each of $v_1, \ldots, v_m$ uniquely identifies $w$. In this talk, we consider the metric dimension of imprimitive distance-regular gr... More
###### Dr. Kamal Lochan Patra, NISER, Bhubaneswar
We consider the following problem: Over the class of all simple connected unicyclic graphs on $n$ vertices with girth $g$ ($n,g$ being fixed), which graph minimizes the Laplacian spectral radius? Let $U_{n,g}$ be the lollipop graph obtained by appending a pendent vertex of a path on $n-g\;(n> g)$ vertices to a verte... More
###### Dr. Ida Kantor, Charles University, Prague
In this talk, we want to represent the vertices of a graph with finite sets in such a way that two vertices are adjacent if and only if their sets are very different" (this is similar, e.g., to the notion of Kneser graphs). More precisely, a {\em $k$-min-difference representation} of $G$ is an assignment of a set ... More
###### Mr. Mustafa Kemal Tural, Middle East Technical University
Given a weighted simple graph, the minimum weighted maximal matching (MWMM) problem is the problem of finding a maximal matching of minimum weight. The MWMM problem is NP-hard in general, but is polynomial-time solvable in some special classes of graphs. For instance, it has been shown that the MWMM problem can be s... More
###### Prof. Irene Sciriha, University of Malta
According to the Source and Sink Potential (SSP) model, for a chosen two--vertex--connection, a molecule is a conductor or an insulator, at the Fermi–-level. Of particular interest are two classes of graphs that have analogous vertex pairs, that is the molecule shows the same behaviour for any two-... More
###### Dr. Bert Hartnell, Saint Mary's University
Rather than guarding a network with a minimum dominating set, consider having two types of monitors available, cameras (can see adjacent nodes) and listeners (can detect the distance to an intruder). Preliminary results for finding the minimum number of such monitors for trees will be outlined. More
###### Mr. Aleksander Kelenc, Faculty of Natural Sciences and Mathematics, University of Maribor
In chemistry, the problem known as similarity searching involves finding a set of molecules that are similar to a given sample molecule. The problem is tackled using graph theory and related algorithmic approaches involving some kind of measure of similarity of two graphs. In this talk we present some results about ... More
###### Mr. Primož Potočnik, University of Ljubljana
Given a finite connected graph $\Gamma$ and a group $G$ acting transitively on the arcs of $\Gamma$, one defines the {\em local group} $G_v^{\Gamma(v)}$ as the permutation group induced by the action of the stabiliser $G_v$ on the neighbourhood $\Gamma(v)$ of a vertex $v$. I will address the following question: ... More
###### Prof. Susan Antoinette van Aardt, University of South Africa
We give a short survey on old and new results on the orders of hypohamiltonian and hypotraceable graphs, digraphs and oriented graphs. In particular we show that there exists a hypohamiltonian oriented graph of order $n$ if and only if $n\geq 9$ and there exists a planar hypotraceable oriented graph of order $n$... More
###### Prof. Mirko Horňák, P.J. Šafárik University Košice
Let $G$ be a graph, $C$ a set of colours and $\varphi:E(G)\to C$ a proper edge colouring of $G$. The $\varphi$-palette of a vertex $v\in V(G)$ is the set $\{\varphi(vw):vw\in E(G)\}$. The $\varphi$-diversity is the number of distinct $\varphi$-palettes of vertices of $G$ and the palette index of $G$ is the minimum o... More
###### Polona Repolusk, University of Maribor, Faculty of natural sciences and mathematics
Given a graph $G$ and a set of $t$ colors $\lbrace 1,2,\ldots , t \rbrace$, assume that we assign an arbitrary subset of these colors to each vertex of $G$. If we require that each vertex to which an empty set is assigned has in its neighborhood all $t$ colors, then this assignment is called a $t$-rainbow dominating... More
###### Prof. Jan van Vuuren, Stellenbosch University
A vertex subset $X\subseteq V$ of a graph $G=(V,E)$ is an {\em independent set} of $G$ if no two vertices in $X$ are adjacent in $G$. The cardinality of a largest independent set of $G$ is called the (vertex) {\em independence number} of $G$. A nonempty graph $G$ is {\em $p$-stable} if $p$ is the largest number of ... More
###### Prof. Ali Iranmanesh, Tarbiat Modares University
Let $G$ be a simple connected $n$-vertex graph with the vertex set $V(G)=\{ v_{1} ,v_{2} ,...,v_{n} \}$ and let ${\rm P} =(p_{1} ,p_{2} ,...,p_{n} )$ be an $n$-tuple of nonnegative integers. The thorn graph $G_{{\rm P} }$ is the graph obtained by attaching $p_{i}$ pendent vertices to the vertex $v_{i}$ of $G$, ... More
###### Mr. Matjaž Krnc, Institute of Mathematics, Physics and Mechanics
The well studied Wiener index $W(G)$ of a graph $G$ is equal to the sum of distances between all pairs of vertices of $G$. Denote by $\mathrm{Im}\left(n\right)$ the set of all values of the Wiener Index over all connected graphs on $n$ vertices. Also, let $\mathcal{I}_{n}$ be the largest interval which is fully... More
###### Dr. Carl Yerger, Davidson College
Given a distribution of pebbles on the vertices of a connected graph $G$, a \textit{pebbling move} is defined as the removal of two pebbles from some vertex and the placement of one of these on an adjacent vertex. The \textit{pebbling number} of a graph $G$ is the smallest integer $k$ such that for each vertex $v$ ... More
###### Grzegorz Kubicki, University of Louisville, USA, and University of Opole, Poland
We want to maximize the number of moves for a random walk on an even cycle before visiting the vertex opposite to the starting position. Our payoff is the number of moves but it is reduced to 0 if we are not able to avoid the opposite vertex. Optimal stopping time and the expected value of the payoff are determined ... More
###### Prof. Russ Woodroofe, Mississippi State University
The lattice of order congruences of a poset P is the subposet O(P) of the lattice of partitions of P, consisting of all partitions that satisfy a certain order-convexity property. The partition lattice is both semi-modular and supersolvable, but Körtesi, Radelecki and Szilágyi gave examples of order congruence latt... More
###### Prof. Tomaž Pisanski, University of Primorska and University of Ljubljana
A maniplex is a discrete structure, introduced in 2012 by Steve Wilson, that generalizes the concept of a map on the one hand, and the concept of an abstract polytope on the other. In a preprint in 2013 Isabel Hubard et al. have defined the notions of orientable and oriented maniplex. In this talk we revisit these... More
###### Mrs. Katarína Hriňáková, Slovak University of Technology in Bratislava
In this talk we will present an enumeration of orientably-regular maps with automorphism group isomorphic to the twisted linear fractional group $M(q^2)$ for any odd prime power $q$. More
###### Prof. Carsten Thomassen, Technical University of Denmark
Let $\Gamma$ be an abelian group and $F$ a set of elements of $\Gamma$. We consider the following general problem: Given a graph $G$, is it possible to give every edge a direction and an element from $F$ such that, at every vertex, the in-sum equals the out-sum. Tutte's flow conjectures and the $(2+\epsilon)$-flow c... More
###### Mr. Ján Karabáš, University of Primorska, Koper and Matej Bel University, Banská Bystrica
An oriented map $M$ is edge-transitive if its group of automorphisms, $\mathrm{Aut}\,M$, acts transitively on the edges of the underlying graph of $M$. The group of orientation-preserving automorphisms, $\mathrm{Aut}^+\,M$, of index at most two of $\mathrm{Aut}\,M$. It follows that the quotient map of an edge... More
###### Prof. Andrey Vasilyev, Sobolev Institute of Mathematics
A sufficient condition for a homogeneous coherent configuration (or simply a scheme) to have the (combinatorial) base of size $2$ is proved. This result is applied to the Cartan scheme of a finite simple group $G$ with BN-pair; by definition, it is the coherent configuration associated with the action of $G$ on the... More
###### Dr. Anamari Nakić, University of Zagreb
A design over the finite field $\mathbb{F}_q$ with parameters $t$-$(v,k,\lambda)_q$ is a pair $(\mathcal{V}, \mathcal{B})$ where $\mathcal{V}$ is the $v$-dimensional vector space over $\mathbb{F}_q$ and $\mathcal{B}$ is a collection of $k$-dimensional subspaces of $\mathcal{V}$, such that each $t$-dimensional subspa... More
###### Prof. Egon Schulte, Northeastern University
Highly symmetric polyhedra-like structures in ordinary euclidean 3-space have a long history of study tracing back to the early days of geometry. With the passage of time, various notions of polyhedra have brought to light new exciting figures intimately related to finite or infinite groups of isometries. In the 197... More
###### Dr. Sanja Rukavina, Department of Mathematics, University of Rijeka
Graphs in which each pair of nonadjacent vertices has at most $k$ paths of minimum length between them are called $k$-geodetic graphs. We will discuss some properties of $k$-geodetic graphs constructed from block designs. LDPC codes based on the adjacency matrix of $k$-geodetic graphs obtained from block designs wi... More
###### Prof. Young Soo Kwon, Yeungnam University
In this talk, we will consider some regular Cayley maps on dihedral groups and their corresponding skew-morphisms. Especially, reflexible regular Cayley maps, reglar Cayley maps having minimum kernel, some properties of skew-morphisms of dihedral groups and some recent related progress will be dealt with. More
###### Dr. Carmen Hernando, Universitat Politècnica de Catalunya
Let $\Pi$ be a partition of the set of vertices of a graph $G$. We denote by $r(u|\Pi)$ the vector of distances from vertex $u$ to the parts of $\Pi$. The partition $\Pi$ is a \emph{resolving partition} of $G$ if $r(u,\Pi)\neq r(v,\Pi)$ for every pair of distinct vertices $u$, $v$. The \emph{partition dimension} ... More
###### Ms. Gulnaz Boruzanli, Ege University
For integers $n\geq 3$ and $1\leq k < n$, the generalized Petersen graph $GP[n,k]$ has $2n$ vertices $\{u_0, u_1, \ldots, u_{n-1}, v_0, v_1, \ldots, v_{n-1}\}$ and $3n$ edges $\allowbreak\{u_iu_{i+1}, v_iv_{i+k}, u_iv_i | i=0, 1, \ldots, n-1; \textrm{addition} \bmod{n}\}$. We investigate the diameter, that is th... More
###### Mr. Ngoc Chi Le, Technische Universität Bergakademie Freiberg
The method of augmenting graphs is a general approach to solve the Maximum Independent Set problem. Our objective is to employ this approach to develop polynomial-time algorithms for some so-called Maximum Set problems, i.e. problems which can be stated as follows. Given a (simple, undirected) graph $G$, find a maxi... More