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2012 | 32 | 4 | 771-782
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Rocznik
Tom
32
Numer
4
Strony
771-782
Opis fizyczny
Daty
wydano
2012
otrzymano
2011-08-12
poprawiono
2012-01-25
zaakceptowano
2012-01-30
Twórcy
  • Department of Mathematics & Computer Science, Shahed University, Tehran, PO Box: 18151-159, Iran
  • Young Researchers Club, Islamic Azad University, Ardabil branch, Ardabil, Iran
Bibliografia
  • [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.
  • [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.
  • [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.
  • [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.
  • [5] I. Gutman and O.E. Polansky, Mathematical Concepts in Organic Chemistry (Springer-Verlag, Berlin, 1986).
  • [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.
  • [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.
  • [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.
  • [11] H. Zhao and X. Li, On the Fibonacci numbers of trees, Fibonacci Quart. 44 (2006) 32-38.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1646
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