# Sharp bounds for the number of matchings in generalized-theta-graphs

Ardeshir Dolati; Somayyeh Golalizadeh

Discussiones Mathematicae Graph Theory (2012)

- Volume: 32, Issue: 4, page 771-782
- ISSN: 2083-5892

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topArdeshir Dolati, and Somayyeh Golalizadeh. "Sharp bounds for the number of matchings in generalized-theta-graphs." Discussiones Mathematicae Graph Theory 32.4 (2012): 771-782. <http://eudml.org/doc/270999>.

@article{ArdeshirDolati2012,

abstract = {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.},

author = {Ardeshir Dolati, Somayyeh Golalizadeh},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {generalized-theta-graph; matching; Fibonacci number; Hosoya index; tricyclic graph; connected graph},

language = {eng},

number = {4},

pages = {771-782},

title = {Sharp bounds for the number of matchings in generalized-theta-graphs},

url = {http://eudml.org/doc/270999},

volume = {32},

year = {2012},

}

TY - JOUR

AU - Ardeshir Dolati

AU - Somayyeh Golalizadeh

TI - Sharp bounds for the number of matchings in generalized-theta-graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2012

VL - 32

IS - 4

SP - 771

EP - 782

AB - 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.

LA - eng

KW - generalized-theta-graph; matching; Fibonacci number; Hosoya index; tricyclic graph; connected graph

UR - http://eudml.org/doc/270999

ER -

## References

top- [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. Zbl1165.05321
- [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. Zbl1141.05049
- [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. Zbl1265.05454
- [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. Zbl1222.05197
- [5] I. Gutman and O.E. Polansky, Mathematical Concepts in Organic Chemistry (Springer-Verlag, Berlin, 1986). Zbl0657.92024
- [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.
- [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. Zbl1156.05328
- [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. Zbl1200.05241
- [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.
- [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. Zbl1218.05073
- [11] H. Zhao and X. Li, On the Fibonacci numbers of trees, Fibonacci Quart. 44 (2006) 32-38. Zbl1133.11011

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