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

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  • Fei, Junqi
  • Tu, Jianhua

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.

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  • Fei, Junqi & Tu, Jianhua, 2018. "Complete characterization of bicyclic graphs with the maximum and second-maximum degree Kirchhoff index," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 118-124.
    • Handle: RePEc:eee:apmaco:v:330:y:2018:i:c:p:118-124
    DOI: 10.1016/j.amc.2018.02.025
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    References listed on IDEAS

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    1. Huang, Jing & Li, Shuchao & Li, Xuechao, 2016. "The normalized Laplacian, degree-Kirchhoff index and spanning trees of the linear polyomino chains," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 324-334.
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    4. He, Weihua & Li, Hao & Xiao, Shuofa, 2017. "On the minimum Kirchhoff index of graphs with a given vertex k-partiteness and edge k-partiteness," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 313-318.
    5. Shi, Yongtang, 2015. "Note on two generalizations of the Randić index," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 1019-1025.
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    Cited by:

    1. Sardar, Muhammad Shoaib & Pan, Xiang-Feng & Xu, Si-Ao, 2020. "Computation of resistance distance and Kirchhoff index of the two classes of silicate networks," Applied Mathematics and Computation, Elsevier, vol. 381(C).
    2. Huang, Guixian & He, Weihua & Tan, Yuanyao, 2019. "Theoretical and computational methods to minimize Kirchhoff index of graphs with a given edge k-partiteness," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 348-357.

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