可迹图的谱充分条件

Spectral sufficient conditions on traceable graphs

设G是一个简单图,A(G),Q(G)以及Q(G)分别为G的邻接矩阵,无符号拉普拉斯矩阵以及距离无符号拉普拉斯矩阵,其最大特征值分别称为G的谱半径,无符号拉普拉斯谱半径以及距离无符号拉普拉斯谱半径.如果图G中有一条包含G中所有顶点的路,则称这条路为哈密顿路;如果图G含有哈密顿路,则称G为可迹图;如果图G含有从任意一点出发的哈密顿路,则称G从任意一点出发都是可迹的.主要研究利用图G的谱半径,无符号拉普拉斯谱半径,以及距离无符号拉普拉斯谱半径,分别给出图G从任意一点出发都是可迹的充分条件.

Let G be a simple graph, A（G）, Q（G） and Q（G） are the adjacency matrix, the signless Laplacian matrix, and the distance signless Laplacian matrix of G, respec- tively. The largest eigenvalues of A（G）, Q（G） and Q（G） are called the spectral radius, the signless Laplacian spectral radius and the distance signless Laplacian spectral radius of G, respectively. A path is called a Hamilton path if it contains all vertices of G. A graph is traceable if it contains a Hamilton path. A graph is traceable from every vertex if it contains a Hamilton path from every vertex. The main research of this paper is to give some sufficient conditions for a graph to be traceable from every vertex in terms of spectral radius, signless Laplacian spectral radius and distance signless Laplacian spectral radius of the graph, respectively.