Arithmetic-geometric matrix of graphs and its applications

The chemical applications of the arithmetic-geometric spectral radius pag(G) and energy Eag(G) of a graph G are explored in this paper. We firstly investigate and compare the pre -diction power of arithmetic-geometric spectral radius, arithmetic-geometric energy, spec-tral radii and energies in some other topological descriptors and some physical proper-ties of octane isomers. It is concluded that the arithmetic-geometric spectral radius is a good indicator in forecasting Acentric Factor, Entropy and two topological descriptors SNar, HNar of octane isomers. Since molecular graphs of octane isomers are trees, we study arithmetic-geometric spectral radius of general trees. We prove that for any tree T of or-der n >= 2 , 2 cos n + 1 < pag(Pn) < pag(T) < pag(Sn) = n pi 2 , with equality holds if and only if T similar to= Pn (the path of order n ) for the lower bound, and if and only if T similar to= Sn (the star of order n ) for the upper bound.(c) 2022 Elsevier Inc. All rights reserved.