图的哈密尔顿连通性和从任意点出发都可迹的充分条件

Sufficient conditions for a graph to be Hamilton-connected and traceable from every vertex

图的哈密尔顿路是指通过图的所有顶点的路.如果图G的任意两点都有一条哈密顿尔路,称此G为哈密尔顿连通的.如果图G从任意点出发都有一条哈密尔顿路,称G从任意点出发都是可迹的.根据图G的边数、谱半径和无符号拉普拉斯谱半径,分别给出哈密尔顿连通图以及从任意点出发都可迹图的一些充分条件.

A path passing through all the vertices of a graph is called a Hamilton path.The graph G is said to be Hamilton-connected if any two vertices of G are connected by a Hamilton path.The graph G is traceable from any vertex if it contains a Hamilton path from every vertex of G.In terms of the edge number,the spectral radius and the signless Laplacian spectral radius of a graph,some sufficient conditions for the graph to be Hamilton-connected and to be traceable from every vertex were presented,respectively.