Normal edge-transitive Cayley graphs on non-abelian groups of order 4p,where p is a prime number  

作　　者：DARAFSHEH Mohammad Reza ASSARI Amir 

机构地区：[1]School of Mathematics,Statistics and Computer Science,College of Science,University of Tehran

出　　处：《Science China Mathematics》2013年第1期213-219,共7页中国科学：数学（英文版）

摘　　要：We determine all connected normal edge-transitive Cayley graphs on non-abelian groups with order 4p, where p is a prime number. As a consequence we prove if IGI = 25p, δ = 0, 1, 2 and p prime, then F 1 Cay（G, S） is a connected normal 1/2 arc-transitive Cayley graph only if G = F4p, where S is an inverse closed generating subset of G which does not contain the identity element of G and F4p is a group with presentation F4p = （a, b ｜aP = b4 = 1, b-lab = a^λ）, where λ2 = -1 （mod p）.We determine all connected normal edge-transitive Cayley graphs on non-abelian groups with order 4p,where p is a prime number.As a consequence we prove if |G|=2δp,δ=0,1,2 and p prime,then Γ=Cay(G,S) is a connected normal 1/2 arc-transitive Cayley graph only if G=F4p,where S is an inverse closed generating subset of G which does not contain the identity element of G and F 4p is a group with presentation F4p = a,b|ap=b4=1,b-1ab=aλ,where λ2≡-1(mod p).

关 键 词：Cayley graph automorphism group normal edge-transitive graph 

分 类 号：O157.5[理学—数学]