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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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/8722383 |
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| author | Wenjie Ning Kun Wang Hassan Raza |
| author_facet | Wenjie Ning Kun Wang Hassan Raza |
| author_sort | Wenjie Ning |
| collection | DOAJ |
| 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 |
| id | doaj-art-6d5cf4f563ad46b09bfd0ac39a1a0e3f |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-6d5cf4f563ad46b09bfd0ac39a1a0e3f2025-02-03T06:44:02ZengWileyJournal of Mathematics2314-47852021-01-01202110.1155/2021/8722383Bicyclic Graphs with the Second-Maximum and Third-Maximum Degree Resistance DistanceWenjie Ning0Kun Wang1Hassan Raza2College of ScienceCollege of Mathematics and Systems ScienceBusiness SchoolLet 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.http://dx.doi.org/10.1155/2021/8722383 |
| spellingShingle | Wenjie Ning Kun Wang Hassan Raza Bicyclic Graphs with the Second-Maximum and Third-Maximum Degree Resistance Distance Journal of Mathematics |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2021/8722383 |
| work_keys_str_mv | AT wenjiening bicyclicgraphswiththesecondmaximumandthirdmaximumdegreeresistancedistance AT kunwang bicyclicgraphswiththesecondmaximumandthirdmaximumdegreeresistancedistance AT hassanraza bicyclicgraphswiththesecondmaximumandthirdmaximumdegreeresistancedistance |