Vertex-transitive Neumaier graphs

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 ۱۰ among vertex-transitive Neumaier graphs.

کلیدواژه ها:

Neumaier graph ، vertex-transitive graph ، Cayley graph ، strongly regular graph