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On the Hosoya index of a family of deterministic recursive trees

Author

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  • Chen, Xufeng
  • Zhang, Jingyuan
  • Sun, Weigang

Abstract

In this paper, we calculate the Hosoya index in a family of deterministic recursive trees with a special feature that includes new nodes which are connected to existing nodes with a certain rule. We then obtain a recursive solution of the Hosoya index based on the operations of a determinant. The computational complexity of our proposed algorithm is O(log2n) with n being the network size, which is lower than that of the existing numerical methods. Finally, we give a weighted tree shrinking method as a graphical interpretation of the recurrence formula for the Hosoya index.

Suggested Citation

  • Chen, Xufeng & Zhang, Jingyuan & Sun, Weigang, 2017. "On the Hosoya index of a family of deterministic recursive trees," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 449-453.
    • Handle: RePEc:eee:phsmap:v:465:y:2017:i:c:p:449-453
    DOI: 10.1016/j.physa.2016.08.026
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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.
    2. Yu Yang & Long Li & Wenhu Wang & Hua Wang, 2020. "On BC-Subtrees in Multi-Fan and Multi-Wheel Graphs," Mathematics, MDPI, vol. 9(1), pages 1-29, December.

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