RELATIONS BETWEEN ARITHMETIC-GEOMETRIC INDEX AND GEOMETRIC-ARITHMETIC INDEX

The arithmetic-geometric index AG(G) and the geometric-arithmetic index GA(G) of a graph G are defined as AG(G) = Sigma uv is an element of E(G) d(G)(u)+d(G)(v)/2 root d(G)(u)d(G)(v) and GA(G) = Sigma uv is an element of E(G) 2 root dG(u)dG(v)/dG(u)+dG(v), where E(G) is the edge set of G, and d(G)(u) and d(G)(v) are the degrees of vertices u and v, respectively. We study relations between Lambda G(G) and G Lambda(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) center dot GA(G). All the bounds are sharp.