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

Discussiones Mathematicae Graph Theory (2006)

- Volume: 26, Issue: 3, page 359-368
- ISSN: 2083-5892

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topMehdi Alaeiyan. "Arc-transitive and s-regular Cayley graphs of valency five on Abelian groups." Discussiones Mathematicae Graph Theory 26.3 (2006): 359-368. <http://eudml.org/doc/270263>.

@article{MehdiAlaeiyan2006,

abstract = {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.},

author = {Mehdi Alaeiyan},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {Cayley graph; normal Cayley graph; arc-transitive; s-regular Cayley graph},

language = {eng},

number = {3},

pages = {359-368},

title = {Arc-transitive and s-regular Cayley graphs of valency five on Abelian groups},

url = {http://eudml.org/doc/270263},

volume = {26},

year = {2006},

}

TY - JOUR

AU - Mehdi Alaeiyan

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

JO - Discussiones Mathematicae Graph Theory

PY - 2006

VL - 26

IS - 3

SP - 359

EP - 368

AB - 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.

LA - eng

KW - Cayley graph; normal Cayley graph; arc-transitive; s-regular Cayley graph

UR - http://eudml.org/doc/270263

ER -

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