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.
Alhevaz, A., & Baghipur, M. (2017). MORE ON EDGE HYPER WIENER INDEX OF GRAPHS. Journal of Algebraic Systems, 4(2), 135-153. doi: 10.22044/jas.2017.854
MLA
A. Alhevaz; M. Baghipur. "MORE ON EDGE HYPER WIENER INDEX OF GRAPHS", Journal of Algebraic Systems, 4, 2, 2017, 135-153. doi: 10.22044/jas.2017.854
HARVARD
Alhevaz, A., Baghipur, M. (2017). 'MORE ON EDGE HYPER WIENER INDEX OF GRAPHS', Journal of Algebraic Systems, 4(2), pp. 135-153. doi: 10.22044/jas.2017.854
VANCOUVER
Alhevaz, A., Baghipur, M. MORE ON EDGE HYPER WIENER INDEX OF GRAPHS. Journal of Algebraic Systems, 2017; 4(2): 135-153. doi: 10.22044/jas.2017.854
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