Complete characterization of bicyclic graphs with the maximum and second-maximum degree Kirchhoff index

Junqi Fei and Jianhua Tu

Applied Mathematics and Computation, 2018, vol. 330, issue C, 118-124

Abstract: The degree Kirchhoff index (or multiplicative degree Kirchhoff index) of a connected simple graph G is defined as S′(G)=∑{u,v}⊆V(G)dG(u)dG(v)RG(u,v), where dG(u) is the degree of a vertex u in G and RG(u, v) is the resistance distance between the vertices u and v. In this paper, we completely characterize the bicyclic graphs of order n ≥ 6 having the maximum degree Kirchhoff index. Moreover, the bicyclic graphs of order n ≥ 7 with the second-maximum degree Kirchhoff index have also been determined.

Keywords: Resistance distance; Degree Kirchhoff index; Bicyclic graphs (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:330:y:2018:i:c:p:118-124

DOI: 10.1016/j.amc.2018.02.025

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