UPPER AND LOWER BOUNDS OF THE FOURTH GEOMETRIC-ARITHMETIC INDEX

Let G be a simple connected graph, and d(i) be the degree of its vertex v(i). In a recent paper, the geometric-arithmetic index was defined as [1]: GA(G) = Sigma 2 root d(i)d(j)/d(i) + d(j) (1) with summation going over all pairs of adjacent vertices. The fourth geometric-arithmetic (GA(4)(G)) index, which was defined in [2], and the definition is: GA(4)(G) = Sigma 2 root e(i)e(j)/e(i) + e(j) (2) with summation going over all pairs of adjacent vertices, and e(i) denotes the eccentricity of its vertex v(i). In this paper, we give some relations between GA(4)(G) index, and other indices like Zagreb indices, and Zagreb eccentricity indices.