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

Abstract

Abstract: 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.

Key words: a kind of weighted adjacency matrix, weighted spectral radius, weighted energy, Nordhaus-Gaddum-type relation

CLC Number:

LU Peng-li, XUE Xiao-yan. Bounds for the spectral radius and energy of a kind of weighted adjacency matrix of graphs[J]. Journal of Lanzhou University of Technology, 2023, 49(1): 144-151.

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