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The Maximum Number of Spanning Trees of a Graph with Given Matching Number

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Abstract

The number of spanning trees of a graph G is the total number of distinct spanning subgraphs of G that are trees. Feng et al. determined the maximum number of spanning trees in the class of connected graphs with n vertices and matching number \(\beta \) for \(2\le \beta \le n/3\) and \(\beta =\lfloor n/2\rfloor \). They also pointed out that it is still an open problem to the case of \(n/3<\beta \le \lfloor n/2\rfloor -1\). In this paper, we solve this problem completely.

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Acknowledgements

The authors would like to thank two referees for their valuable comments which lead to an improvement of the original manuscript.

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Authors and Affiliations

  1. Department of Mathematics, South China Agricultural University, Guangzhou, 510642, China

    Muhuo Liu

  2. School of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou, 510631, P. R. China

    Guangliang Zhang

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

    Kinkar Chandra Das

Authors
  1. Muhuo Liu
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  2. Guangliang Zhang
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  3. Kinkar Chandra Das
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Correspondence to Kinkar Chandra Das.

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Communicated by Rosihan M. Ali.

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Liu, M., Zhang, G. & Das, K.C. The Maximum Number of Spanning Trees of a Graph with Given Matching Number. Bull. Malays. Math. Sci. Soc. 44, 3725–3732 (2021). https://doi.org/10.1007/s40840-021-01142-7

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  • DOI: https://doi.org/10.1007/s40840-021-01142-7

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