CAJ | 학술논문

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)≠φ,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.
대우도G,정의타적중간도M(G)적정점집위V(G)∪ E(G),정점집중적량점x화Y재M(G)중상린당차부당{x,y}∪ E(G)≠φ,병차x화y재G중상린혹자관련.재저편문장중간화료하면저개최근이경득도적정리적증명,즉일개도G적중간도M(G)적보도시합밀돈적당차부당G불시성도,병차G불동구우{K1,2K1,K2,K2 ∪ K1,K3,K3 ∪ K1}중적임의일개도.
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 x and y are joined by an edge if {x,y} ∪ E(G) ≠φ,and x and y are 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,K3,K3 ∪ K1}.