Vertex-transitive Neumaier graphs

Jazaeri, Mojtaba

doi:10.22108/toc.2025.144052.2240

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	Vertex-transitive Neumaier graphs
Transactions on Combinatorics
دوره 15، شماره 3، آذر 2026، صفحه 203-214 اصل مقاله (1.48 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2025.144052.2240
نویسنده
Mojtaba Jazaeri^*
Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran
چکیده
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.
کلیدواژه‌ها
Neumaier graph؛ vertex-transitive graph؛ Cayley graph؛ strongly regular graph

مراجع
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Vertex-transitive Neumaier graphs