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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2021
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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) |
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Mathematics QA1-939 |
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Mathematics QA1-939 Wenjie Ning Kun Wang Hassan Raza Bicyclic Graphs with the Second-Maximum and Third-Maximum Degree Resistance Distance |
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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 |