Cayley图与变换图(Interchange Graph)CAYLEY GRAPHS AND INTERCHANGE GRAPHS
孟吉翔,黄琼湘
摘要(Abstract)：
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。
关键词(KeyWords)： cayley图;变换图;对称群;共轭类
基金项目(Foundation): 国家自然科学基金资助项目
作者(Author): 孟吉翔,黄琼湘
参考文献(References)：
- 1 Davio Witte and Joseph A Gallian.A Survey:Hamiltonian Cycles In Cayley Graphs.Discrete Mathematics,1984;51:293～304
- 2 Bruakli R A.Matrices of Zeros and Ones with Fixed Row and Column Sum Vectors.Linear Algebra and Appl,1980;33:159～231．
- 3 Boesch F and Tindell R.Circulants and Their Connectivities.Journal of Graph Theory,1984;8:487～499
- 4 Doorn E A V.Connectivity of Circulant Digraphs.J Graph Theory,1986;10:9～14
- 5 Meng Jixiang and Huang Qiongxiong.On the Connectivity of Cayley Digraphs,to appear.
- 6 Bermond J C,Favaron O.Hamiltonian Decomposition of Cayley Graphs of Degree 4． J Combi Theory,1989;B(46) :142～158
- 7 Richard A.Brualdi and Li Qao.Small Diameter Interchange Graphs of Classes of Matrices of Zeros and Ones.Linear Algebra and Its Applications,1982;46:177～194
- 8 张福基,张云浒.一类(0,1) -多面体,新疆大学学报,1990;7(4) :1～4
- 9 赫尔M.群论.北京:科学出版社,1981
- 10 邦迪J A,默蒂U S R.图论及其应用.北京:科学出版社,1987
- 11 Watkins M E.Connectivity of Transitive Graph,J Combinatorial Theory,1970;8:23～29
- 12 柯召,魏万迪.组合论(上册),北京:科学出版社,1987
- 13 Biggs N L.Algebraic Graph Theory.Combridge University Press,1974
- 14 Zhang Fuji,Lie Xialiang.Hamilton Cycle of a Type of Interchange Graphs,to appear