2024/08/25 by Mojtaba Jazaeri, Jazaeri, Mojtaba
Computer Science · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2408.13722
openalex publication_date 2024/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
A graph Γ 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 Γ 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.