图的Laplace谱半径的上界

The Upper Bound for the Laplace Spectral Radius of Graphs

设G=(V,E)为n阶简单连通图,D(G)和A(G)分表示图G的度对角矩阵和邻接矩阵,则L(G)=D(G)-A(G)称为图G的Laplace矩阵。利用图的顶点度、最大度、平均二次度和图的公共邻点数,结合非负矩阵谱理论给出了图的Laplace谱半径的新上界,同时给出了达到上界的极图。

Let G = （V ,E） be a simple and connected graph with n v e rt ices , D（G） and A （G ） be the diagonal matrix of vertex degrees and the adjacency matrix ofG respectively. Then the matrix L（ G） = D（ G） - A（ G） is called the Laplace matrix of a graph G . In this paper, the spectral theory of nonnegative matrices was used to present a new upper bound for the laplace spectral radius of graphs in terms of the vertex degree, the largest degree, the average 2-degree and the common neighbors of vertexw and^ . Besides, the extreme graph achieving the upper bound was determined.