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.