Bicyclic Graphs with the Second-Maximum and Third-Maximum Degree Resistance Distance

Wenjie Ning, Kun Wang, Hassan Raza and Francisco Balibrea

Journal of Mathematics, 2021, vol. 2021, 1-11

Abstract: 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.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:8722383

DOI: 10.1155/2021/8722383

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