Journal
JOURNAL OF COMBINATORIAL OPTIMIZATION
Volume 32, Issue 2, Pages 550-562Publisher
SPRINGER
DOI: 10.1007/s10878-015-9882-x
Keywords
Expected value; Hosoya index; Merrifield-Simmon index; Polyphenylene chain
Funding
- Hunan Provincial Natural Science Foundation of China [13JJ3053]
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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.
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