On geometric-arithmetic index of graphs

Let G = (V, E) be a simple connected graph (molecular graph) with vertex set V(G) = {v₁v₂,⋯,v_n} and edge set E(G), where |V(G)| = n and |E(G)| = m. Let d_i be the degree of vertex v_i for i = 1,2,⋯, n. In [1], Vukičević et al. defined a new topological index, named "geometric-arithmetic index" of a graph G, denoted by GA(G) and is defined by mathemetical represented In this paper we obtain the lower and upper bounds on GA(G) of a connected graph and characterize graphs for which these bounds are best possible. Moreover, we give Nordhaus-Gaddum-type results for GA(G) of the graph and its complement, and characterize extremal graphs.