Two-geodesic-transitive Graphs and Vertex-transitive Diameter Two Hexavalent Graphs
摘要
In this paper, we first investigate the family of vertex-transitive diameter 2 hexavalent graphs and particularly completely determine such graphs whose automorphism group is transitive on the set of non-adjacent vertex pairs, and then as an application of the above result, we find all the locally connected 2-geodesic-transitive neighbor hexavalent graphs.