Comparison of the Wiener and Kirchhoff Indices of Random Pentachains

Let G be a connected (molecule) graph. The Wiener index WG and Kirchhoff index KfG of G are defined as the sum of distances and the resistance distances between all unordered pairs of vertices in G, respectively. In this paper, explicit formulae for the expected values of the Wiener and Kirchhoff in...

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Autores principales:	Shouliu Wei, Wai Chee Shiu, Xiaoling Ke, Jianwu Huang
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/f696d77cec6541caa9fe90ca89ab982b
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spelling	oai:doaj.org-article:f696d77cec6541caa9fe90ca89ab982b2021-11-08T02:35:48ZComparison of the Wiener and Kirchhoff Indices of Random Pentachains2314-478510.1155/2021/7523214https://doaj.org/article/f696d77cec6541caa9fe90ca89ab982b2021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/7523214https://doaj.org/toc/2314-4785Let G be a connected (molecule) graph. The Wiener index WG and Kirchhoff index KfG of G are defined as the sum of distances and the resistance distances between all unordered pairs of vertices in G, respectively. In this paper, explicit formulae for the expected values of the Wiener and Kirchhoff indices of random pentachains are derived by the difference equation and recursive method. Based on these formulae, we then make comparisons between the expected values of the Wiener index and the Kirchhoff index in random pentachains and present the average values of the Wiener and Kirchhoff indices with respect to the set of all random pentachains with n pentagons.Shouliu WeiWai Chee ShiuXiaoling KeJianwu HuangHindawi LimitedarticleMathematicsQA1-939ENJournal of Mathematics, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Mathematics QA1-939
spellingShingle	Mathematics QA1-939 Shouliu Wei Wai Chee Shiu Xiaoling Ke Jianwu Huang Comparison of the Wiener and Kirchhoff Indices of Random Pentachains
description	Let G be a connected (molecule) graph. The Wiener index WG and Kirchhoff index KfG of G are defined as the sum of distances and the resistance distances between all unordered pairs of vertices in G, respectively. In this paper, explicit formulae for the expected values of the Wiener and Kirchhoff indices of random pentachains are derived by the difference equation and recursive method. Based on these formulae, we then make comparisons between the expected values of the Wiener index and the Kirchhoff index in random pentachains and present the average values of the Wiener and Kirchhoff indices with respect to the set of all random pentachains with n pentagons.
format	article
author	Shouliu Wei Wai Chee Shiu Xiaoling Ke Jianwu Huang
author_facet	Shouliu Wei Wai Chee Shiu Xiaoling Ke Jianwu Huang
author_sort	Shouliu Wei
title	Comparison of the Wiener and Kirchhoff Indices of Random Pentachains
title_short	Comparison of the Wiener and Kirchhoff Indices of Random Pentachains
title_full	Comparison of the Wiener and Kirchhoff Indices of Random Pentachains
title_fullStr	Comparison of the Wiener and Kirchhoff Indices of Random Pentachains
title_full_unstemmed	Comparison of the Wiener and Kirchhoff Indices of Random Pentachains
title_sort	comparison of the wiener and kirchhoff indices of random pentachains
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/f696d77cec6541caa9fe90ca89ab982b
work_keys_str_mv	AT shouliuwei comparisonofthewienerandkirchhoffindicesofrandompentachains AT waicheeshiu comparisonofthewienerandkirchhoffindicesofrandompentachains AT xiaolingke comparisonofthewienerandkirchhoffindicesofrandompentachains AT jianwuhuang comparisonofthewienerandkirchhoffindicesofrandompentachains
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Comparison of the Wiener and Kirchhoff Indices of Random Pentachains

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