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

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Abstract

The Hosoya index \(m(G)\) and the Merrifield–Simmons index \(i(G)\) of a graph \(G\) are the number of matchings and the number of independent sets in \(G\). 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 \(n\) hexagons.

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Acknowledgments

Project supported by Hunan Provincial Natural Science Foundation of China (13JJ3053).

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Authors and Affiliations

  1. College of Mathematics and Computer Science, Hunan Normal University, Changsha, 410081, Hunan, People’s Republic of China

    Guihua Huang, Meijun Kuang & Hanyuan Deng

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  1. Guihua Huang
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  2. Meijun Kuang
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  3. Hanyuan Deng
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Correspondence to Hanyuan Deng.

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Huang, G., Kuang, M. & Deng, H. The expected values of Hosoya index and Merrifield–Simmons index in a random polyphenylene chain. J Comb Optim 32, 550–562 (2016). https://doi.org/10.1007/s10878-015-9882-x

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  • DOI: https://doi.org/10.1007/s10878-015-9882-x

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