MORE ON EDGE HYPER WIENER INDEX OF GRAPHS

سال انتشار: 1396
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 408

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شناسه ملی سند علمی:

JR_JAS-4-2_005

تاریخ نمایه سازی: 18 تیر 1398

چکیده مقاله:

‎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) 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.

نویسندگان

A. Alhevaz

Department of Mathematics, Shahrood University of Technology, P.O. Box: ۳۱۶- ۳۶۱۹۹۹۵۱۶۱, Shahrood, Iran.

M. Baghipur

Department of Mathematics, Shahrood University of Technology, P.O. Box: ۳۱۶- ۳۶۱۹۹۹۵۱۶۱, Shahrood, Iran.