【摘要】 设D(G)和A(G)分别是图G的度对角矩阵和邻接矩阵,则图G的Laplace矩阵定义为L(G)=D(G)-A(G).利用非负矩阵理论和图论知识给出了两个用图的边数、顶点数,以及顶点的最大度、次大度.最小度表示的L(G)谱半径的新上界,并确定等式成立的极图.最后举例说明这些上界使Laplace谱半径的估计值更小,从而在一定程度上改进了一些文献的结果.更多还原

【Abstract】 Let D(G) and A(G) be the degree diagonal matrix and the adjacency matrix of a graph G,respectively.The Laplacian matrix of G is defined as L(G)=D(G)-A(G).In this paper,two new upper bounds for the Laplacian spectral radius of G in terms of the edge number,the vertex number,the largest degree,the second largest degree and the smallest degree of G are given by applying non-negative matrix theory and graph theory.Moreover,all extremal graphs which have these upper bounds are determined.Finally,two examples are given to show that our upper bounds can obtain smaller estimation value for the Laplacian spectral radius,it means that our upper bounds improve the results in previous papers in a way.更多还原