RELATIONS BETWEEN ARITHMETIC-GEOMETRIC INDEX AND GEOMETRIC-ARITHMETIC INDEX

Abstract

The arithmetic-geometric index AG(G) and the geometric-arithmetic index GA(G) of a graph G are defined as AG(G) = P uv∈E(G) dG(u)+dG(v) 2 √ dG(u)dG(v) and GA(G) = P uv∈E(G) 2 √ dG(u)dG(v) dG(u)+dG(v) , where E(G) is the edge set of G, and dG(u) and dG(v) are the degrees of vertices u and v, respectively. We study relations between AG(G) and GA(G) for graphs G of given size, minimum degree and maximum degree. We present lower and upper bounds on AG(G) + GA(G), AG(G) − GA(G) and AG(G) · GA(G). All the bounds are sharp.