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 ... and ..., 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. [ABSTRACT FROM AUTHOR]