On cubic s-arc transitive Cayley graphs of finite simple groups

Xu, Shang Jin; Fang, Xin; Wang, Jie; Xu, Ming

doi:10.1016/j.ejc.2003.10.015

Cited by 65 publications

(40 citation statements)

References 15 publications

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“…Theorem 1.2 is a direct consequence of Corollary 2.2 and Theorem 1.1. Finally, since a Cayley graph of a finite non-abelian simple group is either normal or core-free, our argument leads to the following well-known result which can be derived from [15,27,28]. Theorem 4.1.…”

Section: Discussionmentioning

confidence: 91%

Cubic s-arc transitive Cayley graphs

2009

Discrete Mathematics

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a b s t r a c tThis paper gives a characterization of connected cubic s-transitive Cayley graphs. It is shown that, for s ≥ 3, every connected cubic s-transitive Cayley graph is a normal cover of one of 13 graphs: three 3-transitive graphs, four 4-transitive graphs and six 5-transitive graphs. Moreover, the argument in this paper also gives another proof for a well-known result which says that all connected cubic arc-transitive Cayley graphs of finite non-abelian simple groups are normal except two 5-transitive Cayley graphs of the alternating group A 47 .

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Section: Discussionmentioning

confidence: 91%

Cubic s-arc transitive Cayley graphs

2009

Discrete Mathematics

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“…On the other hand, we know from [11,12] that for almost finite nonabelian simple groups, except only the alternating group A 47 , their connected cubic s-arc-transitive Cayley graphs are normal and hence s 2. It follows that these graphs are either 1-or 2-arc-transitive.…”

Section: Introductionmentioning

confidence: 98%

Connected cubic s-arc-regular Cayley graphs of finite nonabelian simple groups

Deng

2009

Sci. China Ser. A-Math.

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A graph is said to be s-arc-regular if its full automorphism group acts regularly on the set of its s-arcs. In this paper, we investigate connected cubic s-arc-regular Cayley graphs of finite nonabelian simple groups. Two sufficient and necessary conditions for such graphs to be 1-or 2-arcregular are given and based on the conditions, several infinite families of 1-or 2-arc-regular cubic Cayley graphs of alternating groups are constructed.

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“…For instance, Cayley graphs of valency 3 or 4 of simple groups have been investigated in [6,7,32]; Cayley graphs of valency 4 of certain p-groups are investigated in [8,30]. Refer to [4,20,23,24] for more results regarding edge-transitive graphs of small valencies.…”

Section: Introductionmentioning

confidence: 98%

Tetravalent edge-transitive Cayley graphs with odd number of vertices

Zhang

2006

Journal of Combinatorial Theory, Series B

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A characterisation is given of edge-transitive Cayley graphs of valency 4 on odd number of vertices. The characterisation is then applied to solve several problems in the area of edge-transitive graphs: answering a question proposed by Xu [Automorphism groups and isomorphisms of Cayley graphs, Discrete Math. 182 (1998) 309-319] regarding normal Cayley graphs; providing a method for constructing edge-transitive graphs of valency 4 with arbitrarily large vertex-stabiliser; constructing and characterising a new family of half-transitive graphs. Also this study leads to a construction of the first family of arc-transitive graphs of valency 4 which are non-Cayley graphs and have a 'nice' isomorphic 2-factorisation.

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On cubic s-arc transitive Cayley graphs of finite simple groups

Cited by 65 publications

References 15 publications

Cubic s-arc transitive Cayley graphs

Cubic s-arc transitive Cayley graphs

Connected cubic s-arc-regular Cayley graphs of finite nonabelian simple groups

Tetravalent edge-transitive Cayley graphs with odd number of vertices

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