Science China Mathematics

, 54:1937 | Cite as

Cubic semisymmetric graphs of order 8p 3

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Abstract

A regular edge-transitive graph is said to be semisymmetric if it is not vertex-transitive. By Folkman [J. Combin. Theory 3 (1967), 215–232], there is no semisymmetric graph of order 2p or 2p 2 for a prime p, and by Malnič et al. [Discrete Math. 274 (2004), 187–198], there exists a unique cubic semisymmetric graph of order 2p 3, the so called Gray graph of order 54. In this paper, it is shown that there is no connected cubic semisymmetric graph of order 4p 3 and that there exists a unique cubic semisymmetric graph of order 8p 3, which is a ℤ2 × ℤ2-covering of the Gray graph.

Keywords

edge-transitive graph semisymmetric graph regular covering 

MSC(2000)

05C10 05C25 20B25 
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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of MathematicsBeijing Jiaotong UniversityBeijingChina

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