%0 Journal Article
%T MORE ON EDGE HYPER WIENER INDEX OF GRAPHS
%J Journal of Algebraic Systems
%I Shahrood University of Technology
%Z 2345-5128
%A Alhevaz, A.
%A Baghipur, M.
%D 2017
%\ 01/01/2017
%V 4
%N 2
%P 135-153
%! MORE ON EDGE HYPER WIENER INDEX OF GRAPHS
%K Edge-hyper Wiener index
%K line graph
%K Gutman index
%K connectivity
%K edge-transitive graph
%R 10.22044/jas.2017.854
%X 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: $$WW_{e}(G)=\sum_{\{f,g\}\subseteq E(G)}(d_{e}(f,g|G)+d_{e}^{2}(f,g|G))=\frac{1}{2}\sum_{f\in E(G)}(d_{e}(f|G)+d^{2}_{e}(f|G)),$$ 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) edge-hyper Wiener index in certain graphs. We give also upper and lower bounds for the (first) edge-hyper 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 edge-hyper Wiener index of the some classes of graphs. Our aim in last section is to find a relation between the third edge-hyper Wiener index of a general graph and the hyper Wiener index of its line graph. of two or more graphs and compute edge-hyper Wiener number of some classes of graphs.
%U https://jas.shahroodut.ac.ir/article_854_2486403d0b8da2a0bb248f7cd1fcd96b.pdf