On the spectral radius, energy and Estrada index of the arithmetic–geometric matrix of a graph

Abstract

Let [Formula: see text] be a simple undirected graph with vertex set [Formula: see text]. The arithmetic–geometric matrix [Formula: see text] of a graph [Formula: see text] is defined so that its [Formula: see text]-entry is equal to [Formula: see text] if the vertices [Formula: see text] and [Formula: see text] are adjacent, and zero otherwise, where [Formula: see text] denotes the degree of vertex [Formula: see text] in [Formula: see text]. In this paper, some bounds on the arithmetic–geometric spectral radius and arithmetic–geometric energy are obtained, and the respective extremal graphs are characterized. Moreover, some bounds for the arithmetic–geometric Estrada index involving arithmetic–geometric energy of graphs are determined. Finally, a class of arithmetic–geometric equienergetic graphs is constructed by graph operations.