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

Mehdi Alaeiyan — 2006

Discussiones Mathematicae Graph Theory

Let G be a finite group, and let $1_{G} \notin S \subseteq G$ . 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 $y x^{- 1} \in S$ . Further, if $S = S^{- 1} : = s^{- 1} | s \in S$ , 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...

Semisymmetric cubic graphs of order $4 p^{n}$ .

Alaeiyan, Mehdi; Onagh, B.N. — 2009

Acta Universitatis Apulensis. Mathematics - Informatics

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

Semisymmetric cubic graphs of order 4 p n .

Semisymmetric cubic graphs of order $4 p^{n}$ .