Vertex-transitive Diameter Two Graphs  

作　　者：Wei JIN Li TAN 

机构地区：[1]School of Statistics,Jiangxi University of Finance and Economics,Nanchang 330013,China [2]School of Mathematics and Statistics,HNP-LAMA,Central South University,Changsha 410075,China [3]Research Center of Applied Statistics,Jiangxi University of Finance and Economics,Nanchang 330013,China

出　　处：《Acta Mathematicae Applicatae Sinica》2022年第1期209-222,共14页应用数学学报（英文版）

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)。

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.

关 键 词：vertex-transitive graph DIAMETER automorphism group 

分 类 号：O157.5[理学—数学]