Ademir Hujdurović – Quasi m-Cayley graphs

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.We will present the classifications of quasi 2-

Cayley, strongly quasi 3-Cayley and strongly quasi 4-Cayley arc-transitive circulants.