哈密尔顿图的一些谱充分条件

Some Sufficient Spectral Conditions on Hamiltonian Graphs

图的邻接矩阵和无符号拉普拉斯矩阵的最大特征值分别称为谱半径和无符号拉普拉斯谱半径。由于图的谱容易计算,所以通过图的谱来研究图的结构性质。近年来,利用图的谱研究图的哈密尔顿性已经成为一个前沿热点问题。受此启发,利用图以及补图的谱半径和无符号拉普拉斯谱半径来刻画图的哈密尔顿性,进而得到更好的哈密尔顿图的谱充分条件。

The maximal eigenvalues of graph adjacency matrix and signless Laplacian matrix are called spectral radius and signless Laplacian spectral radius respectively.Since the spectrum of a graph is easy to calculate,it is necessary to use the spectrum of a graph to study its structural properties.In recent years,it has become a hot topic to study the Hamiltonian of graphs by using the spectrum of graphs.Inspired by this,this paper uses spectral radius,signless Laplacian spectral radius of graphs and complementary graphs to characterize the Hamiltonian of graphs.Therefore,we obtains better sufficient spectral conditions of Hamiltonian graphs.