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arXiv · 2408.13722

Vertex-transitive Neumaier graphs

Mojtaba Jazaeri
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Abstract

A graph $\Gamma$ is called edge-regular whenever it is regular and for any two adjacent vertices, the number of their common neighbors is independent of the choice of vertices. A clique $C$ in $\Gamma$ is called regular whenever for any vertex out of $C$, the number of its neighbors in $C$ is independent of the vertex. A Neumaier graph is a non-complete edge-regular graph with a regular clique. In this paper, we study vertex-transitive Neumaier graphs. We give a necessary and sufficient condition under which a vertex-transitive Neumaier graph is strongly regular. We also identify Neumaier Cayley graphs with small valency at most $10$ among vertex-transitive Neumaier graphs.

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Mojtaba Jazaeri. 2024-08-25. Vertex-transitive Neumaier graphs. https://arxiv.org/abs/2408.13722

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