MORE ON EDGE HYPER WIENER INDEX OF GRAPHS
عنوان مقاله: MORE ON EDGE HYPER WIENER INDEX OF GRAPHS
شناسه ملی مقاله: JR_JAS-4-2_005
منتشر شده در شماره 2 دوره 4 فصل در سال 1396
شناسه ملی مقاله: JR_JAS-4-2_005
منتشر شده در شماره 2 دوره 4 فصل در سال 1396
مشخصات نویسندگان مقاله:
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.
خلاصه مقاله:
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.
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.
کلمات کلیدی: Edge-hyper Wiener index, line graph, Gutman index, connectivity, edge-transitive graph
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/893205/