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Computing the clar number of nanotubes and other fullerenes | ||
| Journal of Discrete Mathematics and Its Applications | ||
| مقاله 3، دوره 7، شماره 4، اسفند 2022، صفحه 209-221 اصل مقاله (2.03 M) | ||
| نوع مقاله: Full Length Article | ||
| شناسه دیجیتال (DOI): 10.22061/jdma.2022.843 | ||
| نویسندگان | ||
| Juan Andres Montoya* 1؛ Laura Viviana Cadavid2 | ||
| 1Mathematics, Sciences Universidad Nacional de Colombia Bogota | ||
| 2Mathematics, Sciences, Universidad Nacional de Colombia, Bogota, Colombia | ||
| تاریخ دریافت: 01 آبان 1401، تاریخ بازنگری: 19 آبان 1401، تاریخ پذیرش: 01 آذر 1401 | ||
| چکیده | ||
| We exhibit a polynomial time algorithm that computes the Clar number of any nanotube. This algorithm can be easily extended to one that computes the Clar number of fullerene whose pentagon-clusters are all of even size. It is known that computing the Clar number of planar graphs is NP-hard. It is not known if computing the Clar number of fullerenes is a tractable problem. We show that the latter problem can be suitably approximated in polynomial time, and we also discuss the existence of fpt-algorithms for this important problem of Cheminformatics. | ||
| کلیدواژهها | ||
| fullerene؛ Clar Number؛ Benzonoids؛ Integer programming | ||
| مراجع | ||
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[1] H. Abeledo, G. Atkinson, Unimodularity of the Clar Number Problem, Linear Algebra Appl. 420 (2007) 441-448. [2] M. Ahmadi, E. Farhadi, V. Khorasani, On computing the Clar number of a fullerene using optimization techniques, MATCH Commun. Math. Comput. Chem. 75 (2016) 695-701. [3] E. Berczi-Kovacs, A. Bernath, The complexity of the Clar number problem and an FPT algorithm, TR-2016-20. Egervary Research Group, www.cs.elte.hu/egres, 2016. [4] E. Clar, The Aromatic Sextet,Wiley, New York, 1972. [5] C. Dekker, Carbon nanotubes as molecular quantum wires, Physics Today 52 (5) (1999) 22-28. [6] L. Esperet, F. Kardoˇs, A. King, D. Kr´al, Daniel, S. Norine, Exponentially many perfect matchings in cubic graphs, Adv. Math. 227(4) (2012) 1646-1664. [7] J. Flum , M. Grohe, Parameterized Complexity Theory, Springer Verlag, Heidelberg, 2006. [8] P. Fowler, D. Manolopoulos, An Atlas of Fullerenes, Dover, NewYork, 2007. [9] M. Ghorbani, E. Naserpour, The Clar Number of Fullerene C24n and Carbon Nanocone CNC44[n], Iran. J. Math. Chem. 2(1) (2011) 53-59. [10] M. Jalali-Rad, Which fullerenes are stable?, J. math. nonosci. 5 (2015) 23-29. [11] F. Kardoˇs, D. Kral, J. Miskuf, J. Sereni, Fullerene graphs have exponentially many perfect matching, J. Math. Chem. 46(2) (2009) 443–447. [12] F. Kardoˇs, A computer-assisted proof of Barnette-Goodey conjecture: Not only fullerene graphs are Hamiltonian, SIAM J. Discret. Math. 34(1) (2020) 62–100. [13] P. Kasteleyn, The statistics of dimers on a lattice I: The number of dimer arrangements on a quadratic lattice, Physica 27(12) (1961) 1209–1225. [14] H. Kroto, J. Heath, S. O’Brien, R. Curl, R. Smalley, C60 Buckminsterfullerene, Nature 318 (6042) (1985) 162-163. [15] H. Zhang, D. Ye, Y. Liu, A combination of Clar number and Kekul ´e count as an indicator of relative stability of fullerene isomers of C60, J. Math. Chem. 48 (2010) 733–740. [16] H. Zhang, D. Ye, An upper bound for the Clar number of fullerene graphs, J. Math. Chem. 41(2) (2007) 123-133. | ||
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