# Edge Realizability of Connected Simple Graphs

### Cherif Sellal Polytechnique de Montréal

#### Damir Vukičević University of Split Croatia

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Minisymposium: CHEMICAL GRAPH THEORY

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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