Hosoya Index of Splices, Bridges, and Necklaces

  • Tomislav DošlićEmail author
  • Reza Sharafdini
Part of the Carbon Materials: Chemistry and Physics book series (CMCP, volume 9)


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.


Simple Graph Topological Index Central Vertex Pendent Vertex Lucas Number 
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  1. Ashrafi AR, Hamzeh A, Hossein-Zadeh S (2011) Calculation of some topological indices of splices and links of graphs. J Appl Math Inform 29:327–335Google Scholar
  2. Cyvin SJ, Gutman I (1988) Hosoya index of fused molecules. MATCH Commun Math Comput Chem 23:89–94Google Scholar
  3. Došlić T (2005) Splices, links and their degree-weighted Wiener polynomials. Graph Theory Notes NY 48:47–55Google Scholar
  4. Gutman I, Polansky OE (1986) Mathematical concepts in organic chemistry. Springer, BerlinCrossRefGoogle Scholar
  5. Gutman I, Kolaković N, Cyvin SJ (1989) Hosoya index of some polymers. MATCH Commun Math Comput Chem 24:105–117Google Scholar
  6. Hosoya H (1971) Topological index, a newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons. Bull Chem Soc Jpn 44:2332–2339CrossRefGoogle Scholar
  7. Imrich W, Klavžar S (2000) Product graphs: structure and recognition. Wiley, New YorkGoogle Scholar
  8. Koshy T (2001) Fibonacci and Lucas numbers with applications. Wiley, New YorkCrossRefGoogle Scholar
  9. Mansour T, Schork M (2010) Wiener, hyper-Wiener, detour and hyper-detour indices of bridge and chain graphs. J Math Chem 47:72–98CrossRefGoogle Scholar
  10. Sharafdini R, Gutman I (2013) Splice graphs and their topological indices. Kragujevac J Sci 35:89–98Google Scholar
  11. The Online Encyclopedia of Integer Sequences, OEIS Foundation.
  12. Todeschini R, Consonni V (2000) Handbook of molecular descriptors. Wiley, WeinheimCrossRefGoogle Scholar
  13. Turker L (2003) Contemplation on the Hosoya indices. J Mol Struct (THEOCHEM) 623:75–77CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Faculty of Civil EngineeringUniversity of ZagrebZagrebCroatia
  2. 2.Department of Mathematics, Faculty of Basic SciencesPersian Gulf UniversityBushehrIran

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