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Arc-transitive and s-regular Cayley graphs of valency five on Abelian groups

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Alaeiyan M.

Discussiones Mathematicae Graph Theory

2006

tom 26

nr 3

359-368

Let G be a finite group, and let $1_G ∉ S ⊆ G$. A Cayley di-graph Γ = Cay(G,S) of G relative to S is a di-graph with a vertex set G such that, for x,y ∈ G, the pair (x,y) is an arc if and only if $yx^{-1} ∈ S$. Further, if $S = S^{-1}:= {s^{-1}|s ∈ S}$, then Γ is undirected. Γ is conected if and only if G = ⟨s⟩. A Cayley (di)graph Γ = Cay(G,S) is called normal if the right regular representation of G is a normal subgroup of the automorphism group of Γ. A graph Γ is said to be arc-transitive, if Aut(Γ) is transitive on an arc set. Also, a graph Γ is s-regular if Aut(Γ) acts regularly on the set of s-arcs. In this paper, we first give a complete classification for arc-transitive Cayley graphs of valency five on finite Abelian groups. Moreover, we classify s-regular Cayley graph with valency five on an abelian group for each s ≥ 1.

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1 Discussiones Mathematicae Graph Theory

1 Alaeiyan M.

1 2006

Wyniki wyszukiwania

Arc-transitive and s-regular Cayley graphs of valency five on Abelian groups