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On the Minimum Kirchhoff Index of Unicyclic Graphs with Given Girth and Diameter

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Abstract

An electrical network is often modeled as a graph where every edge of the graph is assumed to be a resistor. The Kirchhoff index Kf(G) of a simple connected graph G is the sum of the resistances between every pair of vertices in G. In this paper, we determine the minimum Kirchhoff index among the unicyclic graphs with given girth and diameter.

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Acknowledgements

This research is supported by National Natural Science Foundation of China (Nos.11801450, 12171272, 11971158), Fundamental Research Funds for the Central Universities (No. D5000210753). Many thanks go to the editor, the reviewers, and the anonymous referees for their valuable and helpful suggestions which greatly improved the presentation of the paper.

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Authors and Affiliations

  1. Department of Electronic Engineering, Tsinghua University, Beijing, 100084, People’s Republic of China

    Feihong Yang

  2. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, People’s Republic of China

    Mei Lu

  3. School of Software, Northwestern Polytechnical University, Xi’an, Shaanxi, 710072, People’s Republic of China

    Jia Guo

Authors
  1. Feihong Yang
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  2. Mei Lu
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  3. Jia Guo
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Correspondence to Jia Guo.

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Communicated by Miin Huey Ang.

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Yang, F., Lu, M. & Guo, J. On the Minimum Kirchhoff Index of Unicyclic Graphs with Given Girth and Diameter. Bull. Malays. Math. Sci. Soc. 45, 1287–1299 (2022). https://doi.org/10.1007/s40840-022-01246-8

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  • DOI: https://doi.org/10.1007/s40840-022-01246-8

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