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

Author

Listed:
  • Wenwen Tian

    (Xi’an Jiaotong University
    Xi’an Jiaotong University
    Xi’an Jiaotong University
    Xi’an Jiaotong University)

  • Fei Zhao

    (Xi’an Jiaotong University
    Xi’an Jiaotong University
    Xi’an Jiaotong University)

  • Zheng Sun

    (Xi’an Jiaotong University
    Xi’an Jiaotong University
    Xi’an Jiaotong University)

  • Xuesong Mei

    (Xi’an Jiaotong University
    Xi’an Jiaotong University
    Xi’an Jiaotong University)

  • Guangde Chen

    (Xi’an Jiaotong University)

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 $$ \Gamma $$ Γ are investigated, and their orderings and extremal trees with respect to these two topological indices are obtained, respectively.

Suggested Citation

  • Wenwen Tian & Fei Zhao & Zheng Sun & Xuesong Mei & Guangde Chen, 2019. "Orderings of a class of trees with respect to the Merrifield–Simmons index and the Hosoya index," Journal of Combinatorial Optimization, Springer, vol. 38(4), pages 1286-1295, November.
    • Handle: RePEc:spr:jcomop:v:38:y:2019:i:4:d:10.1007_s10878-019-00447-5
    DOI: 10.1007/s10878-019-00447-5
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    References listed on IDEAS

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    1. Wan, Pengfei & Tu, Jianhua & Zhang, Shenggui & Li, Binlong, 2018. "Computing the numbers of independent sets and matchings of all sizes for graphs with bounded treewidth," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 42-47.
    2. Guihua Huang & Meijun Kuang & Hanyuan Deng, 2016. "The expected values of Hosoya index and Merrifield–Simmons index in a random polyphenylene chain," Journal of Combinatorial Optimization, Springer, vol. 32(2), pages 550-562, August.
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    Cited by:

    1. Aleksander Vesel, 2021. "Linear Algorithms for the Hosoya Index and Hosoya Matrix of a Tree," Mathematics, MDPI, vol. 9(2), pages 1-11, January.

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