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

TL;DR

This paper classifies all connected cubic edge-transitive bi-Cayley graphs over inner-abelian p-groups for odd primes, advancing understanding of symmetrical graph structures related to specific p-groups.

Contribution

It completes the classification of such graphs over inner-abelian p-groups for odd primes, a previously unresolved problem.

Findings

Complete classification achieved for these graphs

Identification of specific structural properties of the graphs

Extension of known results in symmetrical graph theory

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 paper, we complete the classification of connected cubic edge-transitive bi-Cayley graphs over inner-abelian p-groups for an odd prime p.