Some mathematical properties of the geometric-arithmetic index/coindex of graphs

Abstract

Let G = (V,E), V = {1,2,...,n}, be a simple connected graph of order n, size m with vertex degree sequence d1 ? d2 ? ... ? dn > 0, di = d(vi). The geometric-arithmetic topological index of G is defined as GA(G) = ? i~j 2? didj/di+dj, whereas the geometric-arithmetic coindex as GA?(G) = ? i~/j 2 ? didj/di+dj . New lower bounds for GA(G) and GA(G) in terms of some graph parameters and other invariants are obtained.