Classification of edge-transitive Nest graphs

Abstract

A finite simple graph $$\Gamma $$ Γ is called a Nest graph if it is regular of valency 6 and admits an automorphism with two orbits of the same length such that at least one of the subgraphs induced by these orbits is a cycle. In this paper, we complete classification of the edge-transitive Nest graphs and by this solve the problem posed by Jajcay et al. (Electron J Comb 26:#P2.6, 2019).