图的无符号拉普拉斯谱半径的一个新上下界（英文）

New upper and lower bound for the signless Laplacian spectral radius

D为图的G度序列对角矩阵,A为图的邻接矩阵.Q=D+A为图的无符号拉普拉斯矩阵.Q的最大特征值ξ(G)称为图G的无符号拉普拉斯谱半径.这里将图的2度,平均2度等概念推广到k度与平均k度,得到了图的关于无符号拉普拉斯谱半径的一个新的上、下界.最后举例与图的几个已知经典的界进行了比较.

Let D be the degree diagonal matrix of G,A be the adjacency matrix of G,Q=D+A be the signless Laplacian matrix of G.Let ξ(G) be the signless Laplacian spectral radius of G.Here the degree of graph was extended to k-degree,and average degree to k-average degree of a graph.A new upper and a new lower bound for the signless spectral radius of a graph G was obtained.Comparisons were made of the result with several classical results on the ξ(G).