图的拉普拉斯谱半径

The Laplacian Spectral Radius of Graphs

设G是n阶简单连通图,则L(G)=D(G)-A(G)称为图G的拉普拉斯矩阵,其中A(G)和D(G)分别表示图G的邻接矩阵和度对角矩阵.结合非负矩阵谱理论,利用图的边数、顶点数、最大度、最小度给出了图的拉普拉斯谱半径的新上界,同时给出达到上界的极图,并通过举例将所给的上界与已有的上界作比较,结果说明在一定程度上新上界优于已有结果.

Let G be a simple and connected graph with n vertices,Then L(G)=D(G)-A(G)is called the Laplacian matrix of a graph G,where A(G)and D(G)be the adjacency matrix and the degree-diagonal matrix of G,respectively.The spectral theory of nonnegative matrices was used to present a new upper bound for the Laplacian spectral radius of graphs in terms of the edge number,the vertex number,the largest degree,the smallest degree.Moreover,the extremal graph which achieves the upper bound was determined.Besides,an example is given to illustrate that our result is better than the earlier and recent ones in some sense.