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

Let G be a simple undirected graph with vertex set V(G) = {v(1), v(2), ..., v(n)}. The arithmetic-geometric matrix A(ag) (G) of a graph G is defined so that its (i, j)-entry is equal to d(i)+d(j)/2 root d(i)d(j) if the vertices v(i) and v(j) are adjacent, and zero otherwise, where d(i) denotes the degree of vertex v(i) in G. 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.