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: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 2314-4785 |