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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Autores principales: Wenjie Ning, Kun Wang, Hassan Raza
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Lenguaje:EN
Publicado: Hindawi Limited 2021
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Acceso en línea: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
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