Bicyclic Graphs with the Second-Maximum and Third-Maximum Degree Resistance Distance

Let G=V,E be a connected graph. The resistance distance between two vertices u and v in G, denoted by RGu,v, is the effective resistance between them if each edge of G is assumed to be a unit resistor. The degree resistance distance of G is defined as DRG=∑u,v⊆VGdGu+dGvRGu,v, where dGu is the degree...

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Main Authors:	Wenjie Ning, Kun Wang, Hassan Raza
Format:	article
Language:	EN
Published:	Hindawi Limited 2021
Subjects:	Mathematics QA1-939
Online Access:	https://doaj.org/article/6d5cf4f563ad46b09bfd0ac39a1a0e3f
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spelling	oai:doaj.org-article:6d5cf4f563ad46b09bfd0ac39a1a0e3f2021-11-22T01:09:56ZBicyclic Graphs with the Second-Maximum and Third-Maximum Degree Resistance Distance2314-478510.1155/2021/8722383https://doaj.org/article/6d5cf4f563ad46b09bfd0ac39a1a0e3f2021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/8722383https://doaj.org/toc/2314-4785Let G=V,E be a connected graph. The resistance distance between two vertices u and v in G, denoted by RGu,v, is the effective resistance between them if each edge of G is assumed to be a unit resistor. The degree resistance distance of G is defined as DRG=∑u,v⊆VGdGu+dGvRGu,v, where dGu is the degree of a vertex u in G and RGu,v is the resistance distance between u and v in G. A bicyclic graph is a connected graph G=V,E with E=V+1. This paper completely characterizes the graphs with the second-maximum and third-maximum degree resistance distance among all bicyclic graphs with n≥6 vertices.Wenjie NingKun WangHassan RazaHindawi LimitedarticleMathematicsQA1-939ENJournal of Mathematics, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Mathematics QA1-939
spellingShingle	Mathematics QA1-939 Wenjie Ning Kun Wang Hassan Raza Bicyclic Graphs with the Second-Maximum and Third-Maximum Degree Resistance Distance
description	Let G=V,E be a connected graph. The resistance distance between two vertices u and v in G, denoted by RGu,v, is the effective resistance between them if each edge of G is assumed to be a unit resistor. The degree resistance distance of G is defined as DRG=∑u,v⊆VGdGu+dGvRGu,v, where dGu is the degree of a vertex u in G and RGu,v is the resistance distance between u and v in G. A bicyclic graph is a connected graph G=V,E with E=V+1. This paper completely characterizes the graphs with the second-maximum and third-maximum degree resistance distance among all bicyclic graphs with n≥6 vertices.
format	article
author	Wenjie Ning Kun Wang Hassan Raza
author_facet	Wenjie Ning Kun Wang Hassan Raza
author_sort	Wenjie Ning
title	Bicyclic Graphs with the Second-Maximum and Third-Maximum Degree Resistance Distance
title_short	Bicyclic Graphs with the Second-Maximum and Third-Maximum Degree Resistance Distance
title_full	Bicyclic Graphs with the Second-Maximum and Third-Maximum Degree Resistance Distance
title_fullStr	Bicyclic Graphs with the Second-Maximum and Third-Maximum Degree Resistance Distance
title_full_unstemmed	Bicyclic Graphs with the Second-Maximum and Third-Maximum Degree Resistance Distance
title_sort	bicyclic graphs with the second-maximum and third-maximum degree resistance distance
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/6d5cf4f563ad46b09bfd0ac39a1a0e3f
work_keys_str_mv	AT wenjiening bicyclicgraphswiththesecondmaximumandthirdmaximumdegreeresistancedistance AT kunwang bicyclicgraphswiththesecondmaximumandthirdmaximumdegreeresistancedistance AT hassanraza bicyclicgraphswiththesecondmaximumandthirdmaximumdegreeresistancedistance
_version_	1718418406243303424

Bicyclic Graphs with the Second-Maximum and Third-Maximum Degree Resistance Distance

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