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Comparison between Merrifield-Simmons Index and Wiener Index of Graphs

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Abstract

The Merrifield-Simmons index σ is the total number of independent vertex sets (including the empty set) of the graph G. The Wiener index W is the sum of distances in all unordered pairs of vertices of G. We construct some new graphs satisfying σ > W and W > σ, respectively. In particular, infinite graphs satisfying W > σ are invented with graphs with diameter 2 and infinite ones satisfying σ > W are discovered with so-called universally diametrical graphs.

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Acknowledgements

We thank the referees for their valuable comments on our paper, which have considerably improved the presentation of this paper.

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Authors and Affiliations

  1. College of Mathematics, Nanjing University of Aeronautics & Astronautics, Nanjing, 210016, China

    Ke Xiang Xu & Meng Lu Wang

  2. MIIT Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles, Nanjing, 210016, China

    Ke Xiang Xu & Meng Lu Wang

  3. Department of Mathematics, Sungkyunkwan University, Suwon, 16419, Republic of Korea

    Kinkar Chandra Das

  4. Faculty of Science, University of Kragujevac, P. O. Box 60, 34000, Kragujevac, Serbia

    Ivan Gutman

Authors
  1. Ke Xiang Xu
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  2. Kinkar Chandra Das
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  3. Ivan Gutman
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  4. Meng Lu Wang
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Corresponding author

Correspondence to Kinkar Chandra Das.

Additional information

Kexiang Xu is supported by NNSF of China (Grant No. 11671202) and K. C. Das is supported by National Research Foundation funded by the Korean government (Grant No. 2021R1F1A1050)

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Xu, K.X., Das, K.C., Gutman, I. et al. Comparison between Merrifield-Simmons Index and Wiener Index of Graphs. Acta. Math. Sin.-English Ser. 38, 2220–2230 (2022). https://doi.org/10.1007/s10114-022-0540-9

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  • DOI: https://doi.org/10.1007/s10114-022-0540-9

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