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Linear Algorithms for the Hosoya Index and Hosoya Matrix of a Tree

Author

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  • Aleksander Vesel

    (Faculty of Natural Sciences and Mathematics, University of Maribor, SI-2000 Maribor, Slovenia)

Abstract

The Hosoya index of a graph is defined as the total number of its independent edge sets. This index is an important example of topological indices, a molecular-graph based structure descriptor that is of significant interest in combinatorial chemistry. The Hosoya index inspires the introduction of a matrix associated with a molecular acyclic graph called the Hosoya matrix. We propose a simple linear-time algorithm, which does not require pre-processing, to compute the Hosoya index of an arbitrary tree. A similar approach allows us to show that the Hosoya matrix can be computed in constant time per entry of the matrix.

Suggested Citation

  • Aleksander Vesel, 2021. "Linear Algorithms for the Hosoya Index and Hosoya Matrix of a Tree," Mathematics, MDPI, vol. 9(2), pages 1-11, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:2:p:142-:d:478074
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
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