Quasi m-Cayley circulants

Abstract

A graph Γ is called a quasi m-Cayley graph on a group G if there exists a vertex ∞ ∈ V (Γ ) and a subgroup G of the vertex stabilizer Aut(Γ ) ∞ of the vertex ∞ in the full automorphism group Aut(Γ ) of Γ , such that G acts semiregularly on V (Γ ) ∖ {∞} with m orbits. If the vertex ∞ is adjacent to only one orbit of G on V (Γ ) ∖ {∞} , then Γ is called a strongly quasi m -Cayley graph on G . In this paper complete classifications of quasi 2 -Cayley, quasi 3 -Cayley and strongly quasi 4 -Cayley connected circulants are given.