半二面体群的小度数Cayley图  

Cayley Graphs of Small Valencies of Semi-dihedral Graphs

作　　者：姚俊红[1] 王新中[1] 王长群[1] 

机构地区：[1]郑州大学数学系,河南郑州450052

出　　处：《数学的实践与认识》2009年第6期223-232,共10页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10571013)

摘　　要：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Aut X中正规.研究了4m阶半二面体群G=〈a,b a2m=b2=1,ab=am-1〉的3度和4度Cayley图的正规性,其中m=2r且r>2,并得到了几类非正规的Cayley图.A cayley graph X = Cay（G,S） of group G is said to be normal if R（G）, the group of right multiplication, is normal in Aut X. In this paper, we investigate the normality of all cubic and tetravaluent cayley graphs of semi-dihedral group G of order 4m, where G=（a,b｜a^2m=b^2=1,a^b=a^m-1） and m=2^r, r〉2. In addition, we obtain several infinite families of non-normal cayley graphs of semi-dihedral groups.

关 键 词：CAYLEY图 正规CAYLEY图 半二面体群 

分 类 号：O157.5[理学—数学] O152.1[理学—基础数学]