paper

A classification of two-distance-transitive Cayley graphs over the generalized quaternion groups

arXiv:2504.19130

Abstract

A non-complete graph is \emph{ $2$ -distance-transitive} if, for $i = 1, 2$ and for any two vertex pairs $(u_{1}, v_{1})$ and $(u_{2}, v_{2})$ with the same distance $i$ in the graph, there exists an element of the graph automorphism group that maps $(u_{1}, v_{1})$ to $(u_{2}, v_{2})$ . This is a generalization concept of the classical well-known distance-transitive graphs. In this paper, we completely determine the family of $2$ -distance-transitive Cayley graphs over the generalized quaternion groups.