Neighbour-transitive incidence structures in odd graphs.

Minisymposium: POLYTOPES AND GRAPHS

Content: Given $k>0$ and a set $X$ of size $2k+1$, the odd graph $O_{k+1}$ is a $(k+1)$-regular graph whose vertices are the $k$-sets of $X$ and any two are adjacent if and only if they are disjoint. For a subset $\Gamma$ of $V(O_{k+1})$, there is an incidence structure $D$ between the elements of $X$ and those of $\Gamma$. If we define $\Gamma_1$ as the set of neighbours of $\Gamma$ in $D$, (that is, $\Gamma_1$ is the set of vertices of $O_{k+1}$ that are not in $\Gamma$ and are adjacent in the graph to at least one element of $\Gamma$), then a group of automorphisms of $D$ is neighbour-transitive if it is transitive on $\Gamma_1$. In this talk we will present some results and examples of these incidence structures, which are part of ongoing joint work with Brian Corr, Wei Jin, Cheryl Praeger, and Csaba Schneider.

Back to all abstracts