Study of the Matching Interdiction Problem in Some Molecular Graphs of Dendrimers

  • G. H. ShirdelEmail author
  • N. Kahkeshani
Part of the Carbon Materials: Chemistry and Physics book series (CMCP, volume 9)


The purpose of the matching interdiction problem in a weighted graph G is to remove a subset R* of vertices such that the weight of the maximum matching in the graph \( G-{R}^{*} \) is minimized. The ratio between the difference of the optimal and approximate solutions of this problem from the weight of maximum matching in the graph G, where is denoted by e G , is bounded from above. In this paper, we consider some special classes of molecular graphs. It is shown that the value of e G in these graphs is equal to the maximum value.


Short Path Integer Linear Programming Valid Inequality Molecular Graph Linear Programming Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Akgun I, Tansel BC, Wood RK (2011) The multi-terminal maximum-flow network-interdiction problem. Eur J Oper Res 211:241–251CrossRefGoogle Scholar
  2. Altner DS, Ergun O, Uhan NA (2010) The maximum flow network interdiction problem: valid inequalities, integrality gaps, and approximability. Oper Res Lett 38:33–38CrossRefGoogle Scholar
  3. Ashrafi AR, Cataldo F, Iranmanesh A, Ori O (eds) (2013) Topological modelling of nanostructures and extended systems, Carbon material: chemistry and physics 7. Springer, Dordrecht/New YorkGoogle Scholar
  4. Assimakopoulos N (1987) A network interdiction model for hospital infection control. Comput Biol Med 17:413–422CrossRefGoogle Scholar
  5. Bazgan C, Toubaline S, Tuza Z (2011) The most vital nodes with respect to independent set and vertex cover. Discret Appl Math 159:1915–2204CrossRefGoogle Scholar
  6. Behmaram A, Yousefi-Azari H, Ashrafi AR (2013) On the number of matchings and independent sets in (3,6)-fullerenes. MATCH Commun Math Comput Chem 70:525–532Google Scholar
  7. Corley HW, Sha DY (1982) Most vital links and nodes in weighted network. Oper Res Lett 1:157–160CrossRefGoogle Scholar
  8. Diudea MV, Nagy CL, Bende A (2012) On diamond D5. Struct Chem 23:981–986CrossRefGoogle Scholar
  9. Israeli E, Wood RK (2002) Shortest path network interdiction. Networks 40:97–111CrossRefGoogle Scholar
  10. McMasters AW, Mustin TM (1970) Optimal interdiction of a supply network. Naval Res Log Q 17:261–268CrossRefGoogle Scholar
  11. Newkome GR, Moorefield CN, Vögtle F (2001) Dendrimers and dendrons: concepts, syntheses, applications. Wiley-VCH, WeinheimCrossRefGoogle Scholar
  12. Ratliff HD, Sicilia GT, Lubore SH (1975) Finding the n most vital links in flow networks. Manag Sci 21:531–539CrossRefGoogle Scholar
  13. Shen S, Smith JC, Goli R (2012) Exact interdiction models and algorithms for disconnecting networks via node deletions. Discret Optim 9:172–188CrossRefGoogle Scholar
  14. Wood RK (1993) Deterministic network interdiction. Math Comput Modell 17:1–18CrossRefGoogle Scholar
  15. Yousefi-Azari H, Ashrafi AR (2012) Computing PI index of micelle-like chiral dendrimers. Bulg Chem Commun 44:307–309Google Scholar
  16. Zenklusen R (2010) Matching interdiction. Discret Appl Math 158:1676–1690CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of SciencesUniversity of QomQomIran

Personalised recommendations