Tetravalent edge-transitive Cayley graphs with odd number of vertices

Cai-Heng Li; Z.P. Lu; H. Zhang

doi:10.1016/j.jctb.2005.07.003

Tetravalent edge-transitive Cayley graphs with odd number of vertices

Cai-Heng Li, Z.P. Lu, H. Zhang

Research output: Contribution to journal › Article › peer-review

48 Citations (Scopus)

Abstract

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. (c) 2005 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	164-181
Journal	Journal of combinatorial Theory Series B
Volume	96
Issue number	1
DOIs	https://doi.org/10.1016/j.jctb.2005.07.003
Publication status	Published - 2006

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10.1016/j.jctb.2005.07.003

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abstract = "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. (c) 2005 Elsevier Inc. All rights reserved.",

author = "Cai-Heng Li and Z.P. Lu and H. Zhang",

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AU - Lu, Z.P.

AU - Zhang, H.

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N2 - 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. (c) 2005 Elsevier Inc. All rights reserved.

AB - 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. (c) 2005 Elsevier Inc. All rights reserved.

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SP - 164

EP - 181

JO - Journal of combinatorial Theory Series B

JF - Journal of combinatorial Theory Series B

IS - 1

ER -

Tetravalent edge-transitive Cayley graphs with odd number of vertices

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