more on edge hyper wiener index of graphs

‎let g=(v(g),e(g)) be a simple connected graph with vertex set v(g) and edge‎ ‎set e(g)‎. ‎the (first) edge-hyper wiener index of the graph g is defined as‎: ww_{e}(g)=sum_{{f,g}subseteq e(g)}(d_{e}(f,g|g)+d_{e}^{2}(f,g|g))=frac{1}{2}sum_{fin e(g)}(d_{e}(f|g)+d^{2}_{e}(f|g)),‎ ‎where de(f,g|g) denotes the distance between the edges f=xy and g=uv in e(g) and de(f|g)=∑g€(g)de(f,g|g). ‎in this paper we use a method‎, ‎which applies group theory to graph theory‎, ‎to improving‎ ‎mathematically computation of the (first) edgehyper wiener index in certain graphs‎. ‎we give also upper and lower bounds for the (first) edgehyper wiener index of a graph in terms of its size and gutman index‎. ‎also we investigate products of two or more graphs and compute the second edgehyper wiener index of the some classes of graphs‎. ‎our aim in last section is to find a relation between the third edgehyper wiener index of a general graph and the hyper wiener index of its line graph‎. of two or more graphs and compute edgehyper wiener number of some classes of graphs‎.