MORE ON EDGE HYPER WIENER INDEX OF GRAPHS

Abstract. Let G = (V (G);E(G)) be a simple connected graph with vertex set V (G) and edge set E(G). The (rst) edge-hyper Wiener index of the graph G is dened as: WWe(G) = ? ff;ggE(G) (de(f; gjG) + d2e (f; gjG)) = 1 2 ? f2E(G) (de(fjG) + d2e (fjG)); where de(f; gjG) denotes the distance between the edges f = xy and g = uv in E(G) and de(fjG) = ? g2E(G) de(f; gjG). In this pa- per, we use a method, which applies group theory to graph theory, to improving mathematically computation of the (rst) edge-hyper Wiener index in certain classes of graphs. We give also upper and lower bounds for the (rst) edge-hyper Wiener index of a graph in terms of its size and Gutman index. Our aim in last section is to investigate products of two or more graphs, and compute the second edge-hyper Wiener index of the some classes of graphs.