Journal of Combinatorial Optimization

, Volume 38, Issue 4, pp 1286–1295 | Cite as

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

  • Wenwen Tian
  • Fei ZhaoEmail author
  • Zheng Sun
  • Xuesong Mei
  • Guangde Chen


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.


Graph Tree Merrifield–Simmons index Hosoya index Ordering 



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


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Wenwen Tian
    • 1
    • 2
    • 3
    • 4
  • Fei Zhao
    • 1
    • 2
    • 3
    Email author
  • Zheng Sun
    • 1
    • 2
    • 3
  • Xuesong Mei
    • 1
    • 2
    • 3
  • Guangde Chen
    • 4
  1. 1.State Key Laboratory for Manufacturing System EngineeringXi’an Jiaotong UniversityXi’anChina
  2. 2.Shaanxi Key Laboratory of Intelligent RobotsXi’an Jiaotong UniversityXi’anChina
  3. 3.School of Mechanical EngineeringXi’an Jiaotong UniversityXi’anChina
  4. 4.School of ScienceXi’an Jiaotong UniversityXi’anChina

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