Resistance Distance and Kirchhoff Index for a Class of Graphs

Let G[F,Vk,Hv] be the graph with k pockets, where F is a simple graph of order n≥1, Vk={v1,v2,…,vk} is a subset of the vertex set of F, Hv is a simple graph of order m≥2, and v is a specified vertex of Hv. Also let G[F,Ek,Huv] be the graph with k edge pockets, where F is a simple graph of order n≥2,...

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Main Authors:	WanJun Yin, ZhengFeng Ming, Qun Liu
Format:	Article
Language:	English
Published:	Hindawi Limited 2018-01-01
Series:	Mathematical Problems in Engineering
Online Access:	http://dx.doi.org/10.1155/2018/1028614

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record_format	Article
spelling	doaj-08185f0ae03e485fbbfff5266081cc242020-11-25T00:44:10ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472018-01-01201810.1155/2018/10286141028614Resistance Distance and Kirchhoff Index for a Class of GraphsWanJun Yin0ZhengFeng Ming1Qun Liu2School of Electronic & Mechanical Engineering, Xidian University, Xi’an 710071, ChinaSchool of Electronic & Mechanical Engineering, Xidian University, Xi’an 710071, ChinaSchool of Mathematics and Statistics, Hexi University, Gansu, Zhangye 734000, ChinaLet G[F,Vk,Hv] be the graph with k pockets, where F is a simple graph of order n≥1, Vk={v1,v2,…,vk} is a subset of the vertex set of F, Hv is a simple graph of order m≥2, and v is a specified vertex of Hv. Also let G[F,Ek,Huv] be the graph with k edge pockets, where F is a simple graph of order n≥2, Ek={e1,e2,…ek} is a subset of the edge set of F, Huv is a simple graph of order m≥3, and uv is a specified edge of Huv such that Huv-u is isomorphic to Huv-v. In this paper, we derive closed-form formulas for resistance distance and Kirchhoff index of G[F,Vk,Hv] and G[F,Ek,Huv] in terms of the resistance distance and Kirchhoff index F, Hv and F, Huv, respectively.http://dx.doi.org/10.1155/2018/1028614
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	WanJun Yin ZhengFeng Ming Qun Liu
spellingShingle	WanJun Yin ZhengFeng Ming Qun Liu Resistance Distance and Kirchhoff Index for a Class of Graphs Mathematical Problems in Engineering
author_facet	WanJun Yin ZhengFeng Ming Qun Liu
author_sort	WanJun Yin
title	Resistance Distance and Kirchhoff Index for a Class of Graphs
title_short	Resistance Distance and Kirchhoff Index for a Class of Graphs
title_full	Resistance Distance and Kirchhoff Index for a Class of Graphs
title_fullStr	Resistance Distance and Kirchhoff Index for a Class of Graphs
title_full_unstemmed	Resistance Distance and Kirchhoff Index for a Class of Graphs
title_sort	resistance distance and kirchhoff index for a class of graphs
publisher	Hindawi Limited
series	Mathematical Problems in Engineering
issn	1024-123X 1563-5147
publishDate	2018-01-01
description	Let G[F,Vk,Hv] be the graph with k pockets, where F is a simple graph of order n≥1, Vk={v1,v2,…,vk} is a subset of the vertex set of F, Hv is a simple graph of order m≥2, and v is a specified vertex of Hv. Also let G[F,Ek,Huv] be the graph with k edge pockets, where F is a simple graph of order n≥2, Ek={e1,e2,…ek} is a subset of the edge set of F, Huv is a simple graph of order m≥3, and uv is a specified edge of Huv such that Huv-u is isomorphic to Huv-v. In this paper, we derive closed-form formulas for resistance distance and Kirchhoff index of G[F,Vk,Hv] and G[F,Ek,Huv] in terms of the resistance distance and Kirchhoff index F, Hv and F, Huv, respectively.
url	http://dx.doi.org/10.1155/2018/1028614
work_keys_str_mv	AT wanjunyin resistancedistanceandkirchhoffindexforaclassofgraphs AT zhengfengming resistancedistanceandkirchhoffindexforaclassofgraphs AT qunliu resistancedistanceandkirchhoffindexforaclassofgraphs
_version_	1725275997773758464

Resistance Distance and Kirchhoff Index for a Class of Graphs

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