连通图的拟拉普拉斯谱半径的一个上界

A Bound on Quasi-Laplacian Spectral Radius of Connected Graphs

对于连通图G,矩阵Q(G)=D(G)+A(G)称为图G的拟拉普拉斯矩阵,其中D(G)为图的度对角矩阵,A(G)为图的邻接矩阵.本文利用矩阵的一些性质,推导出连通图的拟拉普拉斯谱半径的一个上界.并将该上界与已有的一些结论结合具体图例作了优越性比较.

Let G be a connected graph, its quasi-Laplacian matrix is Q（G） =D（G） ＋A（ G）, where D（G） is the diagonal matrix of its vertex degrees and A （G） is its adjacency matrix. Using some properties of matrix, a sharp upper bound on the quasi-Laplacian spectral radius of connected graphs is obtained, and the superiority of the upper bound is compared with other bounds through some graphs.