MORE ON EDGE HYPER WIENER INDEX OF GRAPHS | ||
| Journal of Algebraic Systems | ||
| مقاله 5، دوره 4، شماره 2، فروردین 2017، صفحه 135-153 اصل مقاله (184.12 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2017.854 | ||
| نویسندگان | ||
| A. Alhevaz* ؛ M. Baghipur | ||
| Department of Mathematics, Shahrood University of Technology, P.O. Box: 316- 3619995161, Shahrood, Iran. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Edge-hyper Wiener index؛ line graph؛ Gutman index؛ connectivity؛ edge-transitive graph | ||
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