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

Guihua Huang, Meijun Kuang and Hanyuan Deng ()
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Guihua Huang: Hunan Normal University
Meijun Kuang: Hunan Normal University
Hanyuan Deng: Hunan Normal University

Journal of Combinatorial Optimization, 2016, vol. 32, issue 2, No 13, 550-562

Abstract: 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.

Keywords: Expected value; Hosoya index; Merrifield–Simmon index; Polyphenylene chain; 05C12; 05C80; 05C90; 05D40 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10878-015-9882-x

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