Arc-transitive and s-regular Cayley graphs of valency five on Abelian groups
Mehdi Alaeiyan
Discussiones Mathematicae Graph Theory, Tome 26 (2006), p. 359-368 / Harvested from The Polish Digital Mathematics Library
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Let G be a finite group, and let 1G∉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.

Publié le : 2006-01-01
EUDML-ID : urn:eudml:doc:270263 
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Mehdi Alaeiyan. Arc-transitive and s-regular Cayley graphs of valency five on Abelian groups. Discussiones Mathematicae Graph Theory, Tome 26 (2006) pp. 359-368. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1328/

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