关于中间图补图的一个定理的简单证明(英文)A Simple Proof of a Theorem on Complements of Middle Graphs
安新慧;黄琼湘;刘晓平;
摘要(Abstract)：
对于图G ,定义它的中间图M(G)的顶点集为V(G)∪ E(G) ,顶点集中的两点x和y在M(G)中相邻当且仅当{x,y}∪ E(G)≠ ,并且x和y在G中相邻或者关联.在这篇文章中简化了下面这个最近已经得到的定理的证明,即一个图G的中间图M(G)的补图是哈密顿的当且仅当G不是星图,并且G不同构于{K1,2K1, K2, K2∪ K1, K3, K3∪ K1}中的任意一个图.
关键词(KeyWords)： 中间图;补图;哈密顿圈
基金项目(Foundation): The research supported by NSFC(10601044);; Scientific Research Foundation for Young Scholar of Xinjiang University
作者(Author): 安新慧;黄琼湘;刘晓平;
Email:
参考文献(References)：
- [1] An X,Wu B.Hamiltonicity of complements of middle graphs[J].Discrete Math,2007,307: 1178-1184.
- [2] Bondy J A,Murty U S R.Graph Theory with Applications[M].American Elsevier,New York: Macmillan, London,1976.
- [3] Chartrand G,Hevia H,Jarrett E B,Schultz M.Subgraph Distances in Graphs Defined by Edge Transfers[J]. Discrete Math,1997,170: 63-79.
- [4] Hamada T,Yoshimura I.Traversability and connectivity of the middle graph of a graph[J].Discrete Math,1976, 14: 247-255.
- [5] Harary F,Nash-Williams C St J A.On eulerian and hamiltonian graphs and line graphs[J].Canad Math Bull,1965, 8:701-709.
- [6] Wu B,Meng J X.Hamiltonian jump graphs[J].Discrete Math,2004,289: 95-106.