An Infinite Family of One-regular and 4-valent Cayley Graphs of Quasi-dihedral Groups

Abstract：A Cayley graph X＝Cay(G，S)of group G is said to be normal if R(G)，the group of right multiplications，is normal Aut(X).An infinite fanily lf normal one-regular Cayley graphs Cay(G，S)of quasi-dihedral groups G＝2m＝y(tǒng)²＝1，x^y＝x^m+1>is obtained，where S＝{x，x^-2，x^s+1y，x^s-1y}，m＝2s，and s is an even greater than 4.In addition，the nornal and one-regular and 4-valent Cayley graphs of quasi-dihedral groups of order 2^rare classi-fied.It is prouvd thay any 4-valent normal and one-regular Cayley graphs of quasi-dihedral ghoups G of order 2^rare isomorphic to Cay(G，{x，x^-1，x^s+1y，x^s-1y})where s＝2^r-2，r＞3.

Key words：one-regular graph；normal Cayley graph；quasi-dihedral group

CLC number：O 152.1

Article ID：1671-6841(2004)01-0007-05