The unicyclic graphs with maximum degree resistance distance

Tu, Jianhua; Du, Junfeng; Su, Guifu

doi:10.1016/j.amc.2015.06.063

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Denote the Minimum Degree Of Vertices In G By δ(G)1

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“…In [17], Gutman et al [17] presented some properties of D R (G) and characterized the unicyclic graphs with the minimum and second-minimum D R (G). Later, the unicyclic graphs with the maximum and second-maximum D R -value were considered in [19,20]. In [21,22], the cactus graphs with the minimum, the second-minimum, and the thirdminimum D R -values were also completely characterized.…”

Section: Denote the Minimum Degree Of Vertices In G By δ(G)mentioning

confidence: 99%

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

Ning

Wang

Raza

2021

Journal of Mathematics

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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 R G u , 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 D R G = ∑ u , v ⊆ V G d G u + d G v R G u , v , where d G u is the degree of a vertex u in G and R G u , 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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Section: Denote the Minimum Degree Of Vertices In G By δ(G)mentioning

confidence: 99%