A generalized-theta-graph is a graph consisting of a pair of end vertices joined by k (k ≥ 3) internally disjoint paths. We denote the family of all the n-vertex generalized-theta-graphs with k paths between end vertices by Θⁿₖ. In this paper, we determine the sharp lower bound and the sharp upper bound for the total number of matchings of generalized-theta-graphs in Θⁿₖ. In addition, we characterize the graphs in this class of graphs with respect to the mentioned bounds.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1646,
author = {Ardeshir Dolati and Somayyeh Golalizadeh},
title = {Sharp bounds for the number of matchings in generalized-theta-graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {32},
year = {2012},
pages = {771-782},
zbl = {1243.05194},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1646}
}
Ardeshir Dolati; Somayyeh Golalizadeh. Sharp bounds for the number of matchings in generalized-theta-graphs. Discussiones Mathematicae Graph Theory, Tome 32 (2012) pp. 771-782. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1646/
[000] [1] H. Deng, The largest Hosoya index of (n, n + 1)-graphs, Comput. Math. Appl. 56 (2008) 2499-2506, doi: 10.1016/j.camwa.2008.05.020. | Zbl 1165.05321
[001] [2] H. Deng and S. Chen, The extremal unicyclic graphs with respect to Hosoya index and Merrifield-Simmons index, MATCH Commun. Math. Comput. Chem. 59 (2008) 171-190. | Zbl 1141.05049
[002] [3] A. Dolati, M. Haghighat, S. Golalizadeh and M. Safari, The smallest Hosoya index of connected tricyclic graphs, MATCH Commun. Math. Comput. Chem. 65 (2011) 57-70. | Zbl 1265.05454
[003] [4] T. Došlić and F. Måløy, Chain hexagonal cacti: Matchings and independent sets, Discrete Math. 310 (2010) 1676-1690, doi: 10.1016/j.disc.2009.11.026. | Zbl 1222.05197
[004] [5] I. Gutman and O.E. Polansky, Mathematical Concepts in Organic Chemistry (Springer-Verlag, Berlin, 1986). | Zbl 0657.92024
[005] [6] 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, doi: 10.1246/bcsj.44.2332.
[006] [7] H. Hua, Minimizing a class of unicyclic graphs by means of Hosoya index, Math. Comput. Modelling 48 (2008) 940-948, doi: 10.1016/j.mcm.2007.12.003. | Zbl 1156.05328
[007] [8] J. Ou, On extremal unicyclic molecular graphs with maximal Hosoya index, Discrete Appl. Math. 157 (2009) 391-397, doi: 10.1016/j.dam.2008.06.006. | Zbl 1200.05241
[008] [9] A. Syropoulos Mathematics of multisets, Multiset Processing, LNCS 2235, C.S. Calude, G. Păun, G. Rozenberg, A. Salomaa (Eds.), (Springer-Verlag, Berlin, 2001) 347-358, doi: 10.1007/3-540-45523-X₁7.
[009] [10] K. Xu, On the Hosoya index and the Merrifield-Simmons index of graphs with a given clique number, Appl. Math. Lett. 23 (2010) 395-398, doi: 10.1016/j.aml.2009.11.005. | Zbl 1218.05073
[010] [11] H. Zhao and X. Li, On the Fibonacci numbers of trees, Fibonacci Quart. 44 (2006) 32-38. | Zbl 1133.11011