Tetravalent edge-transitive Cayley graphs with odd number of vertices

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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.

Keywords

Cayley graphs
Edge-transitive

Cited by (0)

1

Partially supported by an ARC Discovery Project Grant and a QEII Fellowship.

2

Partially supported by the NNSF and TYYF of China.