On diameter two Cayley graphs

作者：

Highlights：

• This paper studies diameter two Cayley graphs, and these graphs are interesting and important in mathematics.

• The main result shows that the order of diameter 2 Cayley graphs satisfying that Rw is transitive in X2(w) but not in X(w) is unbounded.

• The main result shows that the valency of diameter 2 Cayley graphs satisfying that Rw is transitive in X2(w) but not in X(w) is unbounded.

摘要

•This paper studies diameter two Cayley graphs, and these graphs are interesting and important in mathematics.•The main result shows that the order of diameter 2 Cayley graphs satisfying that Rw is transitive in X2(w) but not in X(w) is unbounded.•The main result shows that the valency of diameter 2 Cayley graphs satisfying that Rw is transitive in X2(w) but not in X(w) is unbounded.

论文关键词：Cayley graph,Diameter,Vertex-transitive

论文评审过程：Received 5 June 2022, Revised 17 July 2022, Accepted 19 July 2022, Available online 26 July 2022, Version of Record 26 July 2022.

论文官网地址：https://doi.org/10.1016/j.amc.2022.127437