可迹图的谱半径条件

Spectral Radius Conditions for Traceable Graph

本文研究的是简单图,它的邻接矩阵是表示顶点之间相邻关系的矩阵,它的最大特征值被定义为图的谱半径。如果图中有一条包含图中所有顶点的路,则称这条路为哈密尔顿路;如果一个图含有哈密顿路,则称该图是可迹图。设图具有最小度条件,本文主要利用图的补图的谱半径给出图是可迹图的充分条件。

In this paper, we study the simple graph. The adjacency matrix represents adjacent relation between vertices of it. The largest eigenvalue of the adjacency matrix of this graph, is called the spectral radius A Hamiltonian path of this graph is a path which contains all vertices of this graph.The graph is called traceable graph if it contains a Hamiltonian path. Let this graph with minimum degree condition, this paper mainly studies some conditions for the graph to be a traceable graph in terms of the spectral radius of its complement.