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Hypercubes defined on n-ary sets, the Erdös–Faber–Lovász conjecture on graph coloring, and the description spaces of polypeptides and RNA

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Abstract

The present study deals with the possibility that N-dimensional hypercubes vertices could be constructed with chosen sets, composed by a given number of n elements. That is by: n-ary sets. Application of this possibility is discussed using as examples the coloring of graphs and the Erdös–Faber–Lovász conjecture, as well as protein and RNA descriptions. The outcome of this discussion induces a possibility to use p-dimensional hypercube vertices themselves as the possible elements of the n-ary sets as generators of N-dimensional hypercubes. Thus, providing: \( n = 2^{p} \).

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References

  1. K. Balasubramaniam, J. Math. Chem. 56, 2707–2723 (2018)

    Article  CAS  Google Scholar 

  2. K. Balasubramanian, J. Math. Chem. 57, 665–689 (2018)

    Google Scholar 

  3. R. Carbó-Dorca, J. Math. Chem. 22, 143–147 (1997)

    Article  Google Scholar 

  4. R. Carbó, B. Calabuig, Molecular similarity and quantum chemistry, in Concepts and Applications of Molecular Similarity, Chapter 6, ed. by M.A. Johnson, G.M. Maggiora (Wiley, New York, 1990), pp. 147–171

    Google Scholar 

  5. R. Carbó, B. Calabuig, Int. J. Quantum Chem. 42, 1695–1709 (1992)

    Article  Google Scholar 

  6. J.B. Kruskal, Proc. Am. Math. Soc. 7, 48–50 (1956)

    Article  Google Scholar 

  7. R. Carbó, Ll. Domingo, Int. J. Quantum Chem. 32, 517–545 (1987)

    Article  Google Scholar 

  8. R. Carbó-Dorca, E. Besalú, L.D. Mercado, J. Comput. Chem. 32, 582–599 (2011)

    Article  CAS  PubMed  Google Scholar 

  9. R. Carbó-Dorca, J. Math. Chem. 52, 1848–1856 (2014)

    Article  CAS  Google Scholar 

  10. R. Carbó-Dorca, J. Math. Chem. 53, 171–182 (2015)

    Article  CAS  Google Scholar 

  11. R. Carbó-Dorca, D. Barragán, WIREs Comput. Mol. Sci. 5, 380–404 (2015)

    Article  CAS  Google Scholar 

  12. R. Carbó-Dorca, J. Math. Sci. Mod. (JMSM) 1, 1–14 (2018)

    Google Scholar 

  13. R. Carbó-Dorca, J. Math. Chem. 33, 227–244 (2003)

    Article  Google Scholar 

  14. R. Carbó-Dorca, J. Math. Chem. 54, 1213–1220 (2016)

    Article  CAS  Google Scholar 

  15. R. Carbó-Dorca, J. Math. Chem. 54, 1798–1809 (2016)

    Article  CAS  Google Scholar 

  16. P. Erdös, Combinatorica 1, 25–42 (1981)

    Article  Google Scholar 

  17. R. Carbó-Dorca, J. Math. Chem. 57, 697–700 (2019).

    Article  CAS  Google Scholar 

  18. F.H. Arnold, Acc. Chem. Res. 31, 125–131 (1998)

    Article  CAS  Google Scholar 

  19. M.A. Maria-Solano, E. Serrano-Hervas, A. Romero-Rivera, J. Iglesias-Fernandez, S. Osuna, Chem. Commun. 54, 6622–6634 (2018)

    Article  CAS  Google Scholar 

  20. R. Carbó, L. Leyda, M. Arnau, Int. J. Quantum Chem. 17, 1185–1189 (1980)

    Article  Google Scholar 

  21. R. Carbó, B. Calabuig, Int. J. Quantum Chem. 42, 1681–1693 (1992)

    Article  Google Scholar 

  22. R. Carbó, E. Besalú, Theoretical foundation of quantum similarity, in Molecular Similarity and Reactivity: From Quantum Chemical to Phenomenological Approaches. Understanding Chemical Reactivity, vol. 14, ed. by R. Carbó (Kluwer Academic Publishers, Amsterdam, 1995), pp. 3–30

    Chapter  Google Scholar 

  23. R. Carbó-Dorca, E. Besalú, J. Mol. Struct. (Theochem) 451, 11–23 (1998)

    Article  Google Scholar 

  24. E. Besalú, X. Gironés, Ll. Amat, R. Carbó-Dorca, Acc. Chem. Res. 35, 289–295 (2002)

    Article  CAS  PubMed  Google Scholar 

  25. P. Bultinck, X. Gironés, R. Carbó-Dorca, Molecular quantum similarity: theory and applications, in Reviews in Computational Chemistry, vol. 21, ed. by K.B. Lipkowitz, R. Larter, T. Cundari (Wiley, Hoboken, 2005), pp. 127–207

    Chapter  Google Scholar 

  26. D. Robert, X. Gironés, R. Carbó-Dorca, J. Chem. Inf. Comput. Sci. 40, 839–846 (2000)

    Article  CAS  PubMed  Google Scholar 

  27. C.S. Lupala, P. Gómez-Gutiérrez, J.J. Pérez, J. Comput. Mol. Des. 30, 85–101 (2016)

    Article  CAS  Google Scholar 

  28. C.S. Lupala, P. Gómez-Gutiérrez, J.J. Pérez, J. Mol. Graph. Mod. 68, 184–196 (2016)

    Article  CAS  Google Scholar 

  29. B. Rasaeifar, P. Gómez-Gutiérrez, J.J. Pérez, Bioorg. Med. Chem. Lett. 218, 29–67 (2018)

    Google Scholar 

  30. M. Kimoto, R.S. Cox 3rd, I. Hirao, Expert Rev. Mol. Diagn. 11, 321–331 (2011)

    Article  CAS  PubMed  Google Scholar 

  31. I. Hirao, M. Kimoto; Proc. Jpn. Acad., Ser. B, 88 (2012) 345-367

  32. I. Hirao, M. Kimoto, R. Yamashige, Acc. Chem. Res. 45, 2055–2065 (2012)

    Article  CAS  PubMed  Google Scholar 

  33. M. Kimoto, R. Yamashige, K. Matsunaga, S. Yokoyama, I. Hirao, Nat. Biotechnol. 31, 453–457 (2013)

    Article  CAS  PubMed  Google Scholar 

  34. M. Kimoto, I. Hirao, Creation of unnatural base pair systems toward new DNA/RNA biotechnologies, in Chemical Biology of Nucleic Acids. RNA Technologies, ed. by V. Erdmann, W. Markiewicz, J. Barciszewski (Springer, Berlin, 2014)

    Google Scholar 

  35. R. Carbó-Dorca, J. Math. Chem. 56, 1353–1356 (2018)

    Article  CAS  Google Scholar 

Download references

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Authors and Affiliations

  1. Institut de Química, Computacional i Catàlisi, Universitat de Girona, 17071, Girona, Catalonia, Spain

    Ramon Carbó-Dorca

  2. Department of Chemistry, Manipal University Jaipur, Dehmi Kalan, Jaipur, Rajasthan, 303007, India

    Tanmoy Chakraborty

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  1. Ramon Carbó-Dorca
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  2. Tanmoy Chakraborty
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Correspondence to Ramon Carbó-Dorca.

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Carbó-Dorca, R., Chakraborty, T. Hypercubes defined on n-ary sets, the Erdös–Faber–Lovász conjecture on graph coloring, and the description spaces of polypeptides and RNA. J Math Chem 57, 2182–2194 (2019). https://doi.org/10.1007/s10910-019-01065-6

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