On the first geometricarithmetic index of graphs
Let G G be a simple connected graph and di d i be the degree of its i i th vertex. In a recent paper [D. Vuki?evi?, B. Furtula, Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges, J. Math. Chem. 46 (2009) 13691376] the first geometricarithmetic index of a graph G G was defined as
geometricarithmetic index graph invariant vertex-degree-based graph invariant degree (of vertex)