一类拟二面体群的三度Cayley图的正规性

Cayley Graphs of Three Valencies of Quasi-dihedral Graphs

有限群G的一个Cayley图X=Cay(G,S)称为正规的,如果右乘变换群R(G)在AutX中正规.决定Cayley图是否正规,对于确定它的自同构群的有重要意义.本文综合运用有限群的知识与图的组合技巧证明了一类4m阶拟二面体群G=〈a,b|a2m=b2=1,ab=am+1〉的3度无向连通Cayley图的正规性,其中m=2r,且r>2,并得到该类正规Cayley图.

A Cayley graph X=Cay（G,S） of a finite group G is normal if R（G）,the group of right multiplications,is normal in Aut X.In this paper,the normality of 3-valent connected Cayley graphs of quasi-dihedral groups of order 4m,G= 〈a,b｜a2m=b2=1,ab=am＋1〉,where m=2r,r2,was proved.In addition,an infinite family of normal Cayley graphs of Quasi-dihedral groups was obtaind.