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

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.

For a graph G, the middle graph M（G） of G is the graph with vertex set V（G） ∪ E（G） in which the vertices .rand yare joined by an edge if （x,y）∪E（G）≠φ, and .rand yare adjacent or incident in G. In this note, we provide a simple proof for a theorem, recently obtained by An and Wu, which says that the complement of middle graph M（G） of a graph G is hamiltonian if and only if G is not a star and is not isomorphic to any graph in {K1.2K1,K2,K2∪K1,K2,K2∪K1）.