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Further Results on the Resistance-Harary Index of Unicyclic Graphs

Author

Listed:
  • Jian Lu

    (School of Mathematical Sciences, Anhui University, Hefei 230601, China)

  • Shu-Bo Chen

    (College of Mathematics, Hunan City University, Yiyang 413000, China)

  • Jia-Bao Liu

    (School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China)

  • Xiang-Feng Pan

    (School of Mathematical Sciences, Anhui University, Hefei 230601, China)

  • Ying-Jie Ji

    (School of Mathematical Sciences, Anhui University, Hefei 230601, China)

Abstract

The Resistance-Harary index of a connected graph G is defined as R H ( G ) = ∑ { u , v } ⊆ V ( G ) 1 r ( u , v ) , where r ( u , v ) is the resistance distance between vertices u and v in G . A graph G is called a unicyclic graph if it contains exactly one cycle and a fully loaded unicyclic graph is a unicyclic graph that no vertex with degree less than three in its unique cycle. Let U ( n ) and U ( n ) be the set of unicyclic graphs and fully loaded unicyclic graphs of order n , respectively. In this paper, we determine the graphs of U ( n ) with second-largest Resistance-Harary index and determine the graphs of U ( n ) with largest Resistance-Harary index.

Suggested Citation

  • Jian Lu & Shu-Bo Chen & Jia-Bao Liu & Xiang-Feng Pan & Ying-Jie Ji, 2019. "Further Results on the Resistance-Harary Index of Unicyclic Graphs," Mathematics, MDPI, vol. 7(2), pages 1-13, February.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:2:p:201-:d:207529
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    References listed on IDEAS

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    1. Liu, Jia-Bao & Pan, Xiang-Feng, 2016. "Minimizing Kirchhoff index among graphs with a given vertex bipartiteness," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 84-88.
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    Cited by:

    1. Frank Werner, 2019. "Discrete Optimization: Theory, Algorithms, and Applications," Mathematics, MDPI, vol. 7(5), pages 1-4, May.

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