Edge Realizability of Connected Simple Graphs

Cherif Sellal
Polytechnique de Montréal

Mustapha Aouchiche
GERAD and HEC Montreal

Gilles Caporossi
GERAD and HEC Montreal

Pierre Hansen
GERAD and HEC Montreal

Damir Vukičević
University of Split Croatia



Content: 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 Mathematical Chemical are to optimization of bound additive topological indices. Algorithms for drawing these graphs are also provided

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