摘要
设s_x是n次对称群,M_x是由s_x的一些奇置换组成的共轭类,对任意n本文得到了Cayley图类Cay(M_x,S_x)的点连通度、直径、Hamiltonian 性及其它一些图论性质,同时本文还发现一类变换图G(R^x(1),S^x(1))与Cay(M,S_x)是同构的图类,(其中R^x(1),S^x(1)分别是n维全1行和、列和向量,M是s_x的对换全体),从而得到这类变换图与Cayley图Cay(M_x,S_x)相平行的一些性质。
Let S_n be the symmetric group of degree n,M_n be a conjugate class of odd permutations of S_n.In
this paper,we investigated the connectivity,diameter,and Hamiltonian properties of Cayley graphs
Cay(M_n,S_n)and proved that the interchange graph G(R^(n)(1),S^(n)(1))is isomorphic to the Cayley
graph Cay(M,S_n)(where R^(n)(1) and S^(n)(1) are the n-dimensional row sum vector and column sum
vector of all ls respectively,M is the set of all transpositions of S_n).Therefore some properties of in-
terchange graphs parallel to those of Cayley graphs are obtained.
出处
《新疆大学学报（自然科学版）》
CAS
1992年第1期5-9,共5页
Journal of Xinjiang University(Natural Science Edition)
基金
国家自然科学基金资助项目
关键词
CAYLEY图
变换图
对称群
共轭类
Cayley graph
interchange graph
symmetric group
conjugate class
