摘要
We investigate the family of vertex-transitive graphs with diameter 2.LetΓbe such a graph.Suppose that its automorphism group is transitive on the set of ordered non-adjacent vertex pairs.Then eitherΓis distance-transitive orΓhas girth at most 4.Moreover,ifΓhas valency 2,thenΓ≌C4 or C5;and for any integer n≥3,there exist such graphsΓof valency n such that its automorphism group is not transitive on the set of arcs.Also,we determine this family of graphs of valency less than 5.Finally,the family of diameter 2 circulants is characterized.
基金
supported by the National Natural Science Foundation of China(12061034,12071484,11661039)
Natural Science Foundation of Jiangxi(20212BAB201010,GJJ190273,20192ACBL21007,2018ACB21001)
Natural Science Foundation of Hunan(2020JJ4675)
China Postdoctoral Science Foundation(2019T120563)。
