一类16p阶群的三度Cayley图的正规性

Cayley Graphs of Three Valencies of Graphs of Order 16p

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.研究了一类16p阶群G=〈a,b|a^(8p)=b^2=1,a^b=a^(4p-1)〉的3度无向连通Cayley图的正规性,其中p为奇素数。

A Cayley graph X = Cay（G, S） of a finite group G is said to be normal if R（G）, the group of right multiplications, is normal in AutX. In this paper, by investigating the nomality, we classify 3-valent connected Cayley graphs of groups of order 16p, G = 〈a, b ｜ α^8p = b^2 = 1,a^b = a4p＋l）, where p is odd prime. In addition we obtain an infinite family of normal and non-normal Cavlev ~raDhs of ~rouDsof order 16p.