Hosoya index of bridge and splice graphs

Document Type : Original Article


Department of Mathematics, Faculty of Basic Sciences, Persian Gulf University, Bushehr 75169, Iran


The Hosoya index of a graph is defined as the total number of the matchings (including the empty edge set) of the graph. In this paper, explicit formulas are given for the Hosoya index of bridge and splice graphs.

Graphical Abstract

Hosoya index of bridge and splice graphs


Main Subjects

[1] A. R. Ashrafi, A. Hamzeh and S. Hossein-zadeh, Calculation of some topological indices of splices and links of  graphs, J. Appl. Math. & Informatics, 29 (1-2) (2011) 327 – 335.
[2] S. J. Cyvin and I. Gutman, Hosoya index of fused molecules, MATCH Commun. Math. Comput. Chem, 23 (1988) 89-94. 
[3] S.J. Cyvin, I. Gutman and N. Kolakovic., Hosoya index of some polymers, MATCH Commun. Math. Comput. Chem., 24 (1989) 89-94.
[4] T. Došlić, Splices, links and their degree-weighted Wiener polynomials, Graph Theory Notes New York, 48 (2005) 47-55.
[5] H. Hosoya, Topological index, a newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons, Bull. Chem. Soc. Jpn., 44 (1971) 2332– 2339.
[6] I. Gutman, O.E. Polansky, Mathematical Concepts in Organic Chemistry, Springer-Verlag, Berlin, 1986.
[7] T. Mansour, M. Schork, Wiener, hyper-Wiener, detour and hyper-detour indices of bridge and chain graphs, J. Math. Chem., 47 (2010) 72–98.
[8] L. Turker. Contemplation on the Hosoya indices, J. Mol. Struct.: THEOCHEM, 623 (2003), 75-77.
[9] R. Todeschini and V. Consonni, Handbook of Molecular Descriptors, Wiley-VCH, Weinheim, 2000.
Volume 2, 1-2
June 2012
Pages 9-13
  • Receive Date: 10 January 2012
  • Revise Date: 20 March 2012
  • Accept Date: 05 May 2012
  • Publish Date: 01 June 2012