图的一种加权邻接矩阵谱半径和能量的界

图G的一种加权邻接矩阵记为A_db(G)=(a^db_ij)_n×n,若顶点v_i和顶点v_j相邻,则$a_{i j}^{d b}=\frac{d_{i}+d_{j}}{d_{i} d_{j}}$, 反之a^db_ij=0.给出图G的加权谱半径的上下界,并在此基础上给出加权谱半径的Nordhaus-Gaddum-type关系.得到了图G的加权能量的几个上下界,并在此基础上给出加权能量的Nordhaus-Gaddum-type关系.

Bounds for the spectral radius and energy of a kind of weighted adjacency matrix of graphs

A kind of weighted adjacency matrix of graph G is denoted by A_db(G)=(a^db_ij)_n×n, where $a_{i j}^{d b}=\frac{d_{i}+d_{j}}{d_{i} d_{j}}$ if the vertices v_i and v_j are adjacent, and a^db_ij=0 otherwise. In this paper, some upper and lower bounds of the weighted spectral radius of graph G are first obtained, and then the Nordhaus-Gaddum-type relation for weighted spectral radius is given. In addition, several upper and lower bounds for the weighted energy are obtained, then, the Nordhaus-Gaddum-type results for the weighted energy are presented.