Cubic edge-transitive bi-Cayley graphs over inner-abelian p-groups

Abstract

A graph is said to be a bi-Cayley graph over a group H if it admits H as a group of automorphisms acting semiregularly on its vertices with two orbits. A non-abelian group is called an inner-abelian group if all of its proper subgroups are abelian. In this article, we complete the classification of connected cubic edge-transitive bi-Cayley graphs over inner-abelian p-groups for an odd prime p.

Keywords:

• bi-Cayley graph
• inner-abelian p-group
• edge-transitive graph

2000 Mathematics subject classification:

• 05C25
• 20B25

Additional information

Funding

This work was partially supported by the National Natural Science Foundation of China (11671030,11271012) and the Fundamental Research Funds for the Central Universities (2015JBM110).