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

摘要

The Hosoya index and the Merrifield-Simmons index of a graph are the number of matchings and the number of independent sets in . 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 DoliA double dagger 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 hexagons.