Vertex-transitive Diameter Two Graphs

• 作者: Wei JIN Li TAN
• 来源期刊: 应用数学学报（英文版）
• 年，卷（期）: 2022,（1）
• 页码范围: 209-222
• 页数: 14页
• 语种: 英文

摘要

We investigate the family of vertex-transitive graphs with diameter 2.Let Γ be such a graph.Suppose that its automorphism group is transitive on the set of ordered non-adjacent vertex pairs.Then eitherΓ is distance-transitive or Γ has girth at most 4.Moreover,if Γ has valency 2,then Γ ≌ C4 or C5;and for any integer n≥3,there exist such graphs Γ of 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.