Abstract
The Hosoya index Z(G) of a graph G is the total number of matchings in G. We present explicit formulas for the Hosoya indices of several classes of graphs that arise from simpler graphs by repeating application of two simple operations.
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References
Ashrafi AR, Hamzeh A, Hossein-Zadeh S (2011) Calculation of some topological indices of splices and links of graphs. J Appl Math Inform 29:327–335
Cyvin SJ, Gutman I (1988) Hosoya index of fused molecules. MATCH Commun Math Comput Chem 23:89–94
Došlić T (2005) Splices, links and their degree-weighted Wiener polynomials. Graph Theory Notes NY 48:47–55
Gutman I, Polansky OE (1986) Mathematical concepts in organic chemistry. Springer, Berlin
Gutman I, Kolaković N, Cyvin SJ (1989) Hosoya index of some polymers. MATCH Commun Math Comput Chem 24:105–117
Hosoya H (1971) Topological index, a newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons. Bull Chem Soc Jpn 44:2332–2339
Imrich W, Klavžar S (2000) Product graphs: structure and recognition. Wiley, New York
Koshy T (2001) Fibonacci and Lucas numbers with applications. Wiley, New York
Mansour T, Schork M (2010) Wiener, hyper-Wiener, detour and hyper-detour indices of bridge and chain graphs. J Math Chem 47:72–98
Sharafdini R, Gutman I (2013) Splice graphs and their topological indices. Kragujevac J Sci 35:89–98
The Online Encyclopedia of Integer Sequences, OEIS Foundation. http://oeis.org
Todeschini R, Consonni V (2000) Handbook of molecular descriptors. Wiley, Weinheim
Turker L (2003) Contemplation on the Hosoya indices. J Mol Struct (THEOCHEM) 623:75–77
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Došlić, T., Sharafdini, R. (2016). Hosoya Index of Splices, Bridges, and Necklaces. In: Ashrafi, A., Diudea, M. (eds) Distance, Symmetry, and Topology in Carbon Nanomaterials. Carbon Materials: Chemistry and Physics, vol 9. Springer, Cham. https://doi.org/10.1007/978-3-319-31584-3_10
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DOI: https://doi.org/10.1007/978-3-319-31584-3_10
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