关于Hamilton图的充分必要条件

On fully essential condition of Hamilton Graph

引入与图G具有相同连通性的图G的相关简单图GR 的概念 ,并通过对GR 的邻接矩阵的恒式的研究 ,给出了任意图G (无向、有向、混合 )是Hamilton图的充分必要条件 ,得到了以下主要结论 :定理 :图G是Hamilton图的充分必要条件 ,是图G的相关简单图GR 的邻接矩阵的恒式perGR 不为 0。推论 :若图G的相关简单图GR 的邻接矩阵的行列式不为 0 ,则图G必是Hamilton图。

This article quotes the concept from the simple Graph G R related to Graph G which has the same coherence with Graph G.It makes an investigation into the constant formula of adjacency matrix of Graph G R and give out any graphs(undirection,direction,compound)to be the fully essential condition of Hamilton Graph.It draws the following conclusions that Graph G is the fully essential condition of Hamilton Graph and if PerG R si not zero,Graph G is the constant formula of adjacency matrix of simple Graph G R related to Graph G.His inference is that Graph G is sure to be Hamilton Graph if the row formula of adjacency matrix of the simple Graph G R related to Graph G is not zero.