Cubic semisymmetric graphs of order 8p^3  

作　　者：HUA XiaoHui FENG YanQuan 

机构地区：[1]Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China

出　　处：《Science China Mathematics》2011年第9期1937-1949,共13页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No.10871021);the Specialized Research Fund for the Doctoral Program of Higher Education in China (Grant No.20060004026)

摘　　要：A regular edge-transitive graph is said to be semisymmetric if it is mot 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 Malni6 et al. [Discrete Math. 274 （2004）, 18-198], there exists a unique cubic semisymmetrie graph of order 2p3, 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 8p3, which is a Z2 × Z2-covering of the Gray graph.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 Malni 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 Z 2 × Z 2-covering of the Gray graph.

关 键 词：edge-transitive graph semisymmetric graph regular covering 

分 类 号：O121.5[理学—数学] O158[理学—基础数学]