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The expected values of Hosoya index and Merrifield–Simmons index in a random polyphenylene chain

Author

Listed:
  • Guihua Huang

    (Hunan Normal University)

  • Meijun Kuang

    (Hunan Normal University)

  • Hanyuan Deng

    (Hunan Normal University)

Abstract

The Hosoya index $$m(G)$$ m ( G ) and the Merrifield–Simmons index $$i(G)$$ i ( G ) of a graph $$G$$ G are the number of matchings and the number of independent sets in $$G$$ G . In this paper, we establish exact formulas for the expected values of the Hosoya index and Merrifield–Simmons index of a random polyphenylene chain, and generalize the results of Došlić and Litz (MATCH Commun Math Comput Chem 67:313–330, 2012). Moreover, we obtain the average values of the Hosoya index and the Merrifield–Simmons index with respect to the set of all polyphenylene chains with $$n$$ n hexagons.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:32:y:2016:i:2:d:10.1007_s10878-015-9882-x
    DOI: 10.1007/s10878-015-9882-x
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    Cited by:

    1. 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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