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Orderings of a class of trees with respect to the Merrifield–Simmons index and the Hosoya index

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Abstract

The Merrifield–Simmons index and the Hosoya index are two prominent molecular graph descriptors in mathematical chemistry. The Merrifield–Simmons index of a graph is defined as the total number of the independent sets of the graph and the Hosoya index of a graph is defined as the total number of the matchings of the graph. In this paper, the Merrifield–Simmons index and the Hosoya index of a class of trees \( \Gamma \) are investigated, and their orderings and extremal trees with respect to these two topological indices are obtained, respectively.

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Acknowledgements

The authors would like to thanks the referees for giving many valuable comments and suggestions on improving this paper.

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Authors and Affiliations

  1. State Key Laboratory for Manufacturing System Engineering, Xi’an Jiaotong University, Xi’an, 710049, Shaanxi, China

    Wenwen Tian, Fei Zhao, Zheng Sun & Xuesong Mei

  2. Shaanxi Key Laboratory of Intelligent Robots, Xi’an Jiaotong University, Xi’an, 710049, Shaanxi, China

    Wenwen Tian, Fei Zhao, Zheng Sun & Xuesong Mei

  3. School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an, 710049, Shaanxi, China

    Wenwen Tian, Fei Zhao, Zheng Sun & Xuesong Mei

  4. School of Science, Xi’an Jiaotong University, Xi’an, 710049, Shaanxi, China

    Wenwen Tian & Guangde Chen

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  1. Wenwen Tian
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  2. Fei Zhao
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  3. Zheng Sun
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  4. Xuesong Mei
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Correspondence to Fei Zhao.

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Tian, W., Zhao, F., Sun, Z. et al. Orderings of a class of trees with respect to the Merrifield–Simmons index and the Hosoya index. J Comb Optim 38, 1286–1295 (2019). https://doi.org/10.1007/s10878-019-00447-5

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  • DOI: https://doi.org/10.1007/s10878-019-00447-5

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