图和补图的无号拉普拉斯谱半径之和的2个新上界

Two New Upper Bounds on the Sum of the Signless Laplacian Spectral Radius of A Simple Graph and Its Complement

图G=(V,E)为n阶有限图,A和D分别表示图G的邻接矩阵及度矩阵。R=D+A称为图G的无号拉普拉斯矩阵。利用代数方法和微积分中函数极值条件,对图和补图的无号拉普拉斯谱半径之和的上界进行了估计,得出了2个新的上界。

Let G=(V,E)be a finite graph with n vertices,the matrix A,D denote the adjacency matrix and the diagonal matrix of a graph G,respectively.The matrix D+A is called the signless Laplacian.In the paper,we consider two new upper bounds on the sum of the signless laplacian spectral radius of a simple graph and its complement by means of algebraic method and the condition of maxium and minimum of a function.