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 |
| Langue: | EN |
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Hindawi Limited
2021
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| Accès en ligne: | https://doaj.org/article/6d5cf4f563ad46b09bfd0ac39a1a0e3f |
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| Résumé: | 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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