The Hyper-Wiener Index of Trees of Order n with Diameter d

The Hyper-Wiener Index of Trees of Order n with Diameter d

The hyper-Wiener index is a kind of extension of the Wiener index, used for predicting physicochemical properties of organic compounds. The hyper-Wiener index WW(G) is defined as WW(G)=1/2∑u,v∈VGdGu,v+dG2u,v with the summation going over all pairs of vertices in G, and dGu,v denotes the distance of...

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Main Authors: Gaixiang Cai, Guidong Yu, Jinde Cao, Ahmad Alsaedi, Fuad Alsaadi
Format: Article
Language:English
Published: Hindawi Limited 2016-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2016/7241349
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spelling doaj-8f91b756dcf74a36b53bbcee5adea4462020-11-24T21:04:40ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2016-01-01201610.1155/2016/72413497241349The Hyper-Wiener Index of Trees of Order n with Diameter dGaixiang Cai0Guidong Yu1Jinde Cao2Ahmad Alsaedi3Fuad Alsaadi4School of Mathematics & Computation Sciences, Anqing Normal University, Anqing 246011, ChinaSchool of Mathematics & Computation Sciences, Anqing Normal University, Anqing 246011, ChinaDepartment of Mathematics, Southeast University, Nanjing, Jiangsu 210096, ChinaFaculty of Science, King Abdulaziz University, Jeddah 21589, Saudi ArabiaDepartment of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi ArabiaThe hyper-Wiener index is a kind of extension of the Wiener index, used for predicting physicochemical properties of organic compounds. The hyper-Wiener index WW(G) is defined as WW(G)=1/2∑u,v∈VGdGu,v+dG2u,v with the summation going over all pairs of vertices in G, and dGu,v denotes the distance of the two vertices u and v in the graph G. In this paper, we obtain the second-minimum hyper-Wiener indices among all the trees with n vertices and diameter d and characterize the corresponding extremal graphs.http://dx.doi.org/10.1155/2016/7241349
collection DOAJ
language English
format Article
sources DOAJ
author Gaixiang Cai
Guidong Yu
Jinde Cao
Ahmad Alsaedi
Fuad Alsaadi
spellingShingle Gaixiang Cai
Guidong Yu
Jinde Cao
Ahmad Alsaedi
Fuad Alsaadi
The Hyper-Wiener Index of Trees of Order n with Diameter d
Discrete Dynamics in Nature and Society
author_facet Gaixiang Cai
Guidong Yu
Jinde Cao
Ahmad Alsaedi
Fuad Alsaadi
author_sort Gaixiang Cai
title The Hyper-Wiener Index of Trees of Order n with Diameter d
title_short The Hyper-Wiener Index of Trees of Order n with Diameter d
title_full The Hyper-Wiener Index of Trees of Order n with Diameter d
title_fullStr The Hyper-Wiener Index of Trees of Order n with Diameter d
title_full_unstemmed The Hyper-Wiener Index of Trees of Order n with Diameter d
title_sort hyper-wiener index of trees of order n with diameter d
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2016-01-01
description The hyper-Wiener index is a kind of extension of the Wiener index, used for predicting physicochemical properties of organic compounds. The hyper-Wiener index WW(G) is defined as WW(G)=1/2∑u,v∈VGdGu,v+dG2u,v with the summation going over all pairs of vertices in G, and dGu,v denotes the distance of the two vertices u and v in the graph G. In this paper, we obtain the second-minimum hyper-Wiener indices among all the trees with n vertices and diameter d and characterize the corresponding extremal graphs.
url http://dx.doi.org/10.1155/2016/7241349
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