Some Mathematical Properties of the Geometric-Arithmetic Index/Coindex of Graphs

Let G = (V, E), V = {1, 2, ... , n}, be a simple connected graph of order n, size m with vertex degree sequence d(1) >= d(2) >= center dot center dot center dot >= d(n) > 0, d(i) = d(v(i)). The geometric-arithmetic topological index of G is defined as GA(G) = Sigma(i similar to j) 2 root d(i)d(j)/d(i)+d(j) , whereas thegeometric-arithmetic coindex as (GA) over bar (G) = Sigma(i(sic)j) 2 root d(i)d(j)/d(i)similar to d(j). New lower bounds for GA(G) and GA(G) in terms of some graph parameters and other invariants are obtained.