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The Kirchhoff indices and the matching numbers of unicyclic graphs

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  • Qi, Xuli
  • Zhou, Bo
  • Du, Zhibin

Abstract

The Kirchhoff index of a connected graph is the sum of resistance distances between all unordered pairs of vertices in the graph. In this paper, we determine the minimum Kirchhoff index among the unicyclic graphs with fixed number of vertices and matching number, and characterize the extremal graphs.

Suggested Citation

  • Qi, Xuli & Zhou, Bo & Du, Zhibin, 2016. "The Kirchhoff indices and the matching numbers of unicyclic graphs," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 464-480.
    • Handle: RePEc:eee:apmaco:v:289:y:2016:i:c:p:464-480
    DOI: 10.1016/j.amc.2016.05.003
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    Citations

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    Cited by:

    1. 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.
    2. Cui, Qing & Zhong, Lingping, 2017. "The general Randić index of trees with given number of pendent vertices," Applied Mathematics and Computation, Elsevier, vol. 302(C), pages 111-121.
    3. Yang, Yujun & Cao, Yuliang & Yao, Haiyuan & Li, Jing, 2018. "Solution to a conjecture on a Nordhaus–Gaddum type result for the Kirchhoff index," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 241-249.
    4. 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.
    5. 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.

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