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arXiv · 2401.15411

On extremal (almost) edge-girth-regular graphs

Gabriela Araujo-Pardo·György Kiss·István Porupsánszki
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Abstract

A $k$-regular graph of girth $g$ is called edge-girth-regular graph, shortly egr-graph, if each of its edges is contained in exactly $λ$ distinct $g-$cycles. An egr-graph is called extremal for the triple $(k, g, λ)$ if has the smallest possible order. We prove that some graphs arising from incidence graphs of finite planes are extremal egr-graphs. We also prove new lower bounds on the order of egr-graphs.

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Gabriela Araujo-Pardo, György Kiss, István Porupsánszki. 2024-01-27. On extremal (almost) edge-girth-regular graphs. https://arxiv.org/abs/2401.15411

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