Skip to main content
Log in

Permutational isomers on a molecular skeleton with neighbor-excluding ligands

  • Original Paper
  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

An Erratum to this article was published on 20 December 2008

Abstract

Permutational isomers of ligands substituted on a molecular skeleton are studied under a condition on the ligand placement which excludes a second ligand of the same type at a neighboring skeletal site. General theory to treat such a circumstance is developed to identify a correspondence between isomers and suitable double cosets of groups involving permutations of ligands amongst skeletal sites. Then this theory is illustratively applied for a selection of skeletons, including an experimentally realized hexamalono-buckminsterfullerene skeleton, with 12 ligation locations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Polya G.: Zeit. Kryst. A 93, 414–443 (1936)

    Google Scholar 

  • Polya G.: Vierteljschr. Naturforsch. Ges. (Zurich) 81, 243–258 (1936)

    CAS  Google Scholar 

  • Polya G.: Acta Math. 68, 145–254 (1937)

    Article  Google Scholar 

  • Balaban, A.T. (eds): Chemical Applications of Graph Theory. Academic Press, NY (1975)

    Google Scholar 

  • S. El-Basil, A. Kerber (Special editors), Commun. Math. Comput. Chem. 46, (2002)

  • Polya G., Read R.C.: Combinatorial Enumeration of Groups, Graphs, and Chemical Compounds. Springer-Verlag, Berlin (1987)

    Google Scholar 

  • Balasubramanian K.: Chem. Rev. 85, 599–618 (1985)

    Article  CAS  Google Scholar 

  • Trinajstic N., Nikolic S., Knop J.V., Muller W.R., Szymanski K.: Computational Chemical Graph Theory: Characterization, Enumeration, and Generation of Chemical Structures by Computer Methods. Horwood/Simon & Schuster, New York (1991)

    Google Scholar 

  • El-Basil S.: Commun. Math. Chem. (MATCH) 46, 7–23 (2002)

    CAS  Google Scholar 

  • Kerber A.: Commun. Math. Chem. (MATCH) 46, 151–198 (2002)

    CAS  Google Scholar 

  • Fujita S.: Symmetry and Combinatorial Enumeration in Chemistry. Springer-Verlag, Berlin (1991)

    Google Scholar 

  • El-Basil S.: Combinatorial Organic Chemistry. Nova Sci. Pub., NY (1999)

    Google Scholar 

  • Kerber A.: Applied Finite Group Actions. Springer-Verlag, Berlin (1999)

    Google Scholar 

  • Ruch E., Hasselbarth W., Richter B.: Theor. Chim. Acta. 19, 288–300 (1970)

    Article  CAS  Google Scholar 

  • N.G. De Bruijn, in Applied Combinatorial Mathematics, ed. by E.F. Beckenbach (Wiley, NY, 1964), pp. 144–184

  • Ruch E., Hasselbarth W., Klein D.J., Seligman T.H.: J. Math. Phys. 21, 951–953 (1980)

    Article  Google Scholar 

  • Hasselbarth W., Ruch E.: Israel J. Chem. 15, 112–115 (1976/77)

    Google Scholar 

  • Klein D.J., Cowley A.H.: J. Am. Chem. Soc. 100, 2593–2599 (1978)

    Article  CAS  Google Scholar 

  • Klein D.J., Misra A.: Commun. Math. Chem. (MATCH) 46, 45–69 (2001)

    Google Scholar 

  • DeBruijn N.G.: K. Ned. Akad. Wet. Proc. A. 62, 59–69 (1956)

    Google Scholar 

  • Harary F., Palmer E.: J. Comb. Theory 1, 157–173 (1966)

    Article  Google Scholar 

  • Read R.C: J. London Math. Soc. 34, 417–436 (1959)

    Article  Google Scholar 

  • Williamson S.G.: J. London Math. Soc. 3, 411–421 (1971)

    Article  Google Scholar 

  • White D.E.: Linear Multilinear Alg. 7, 299–315 (1979)

    Article  Google Scholar 

  • Cerar J., Pompe M., Gucek M., Cerkovnik J., Skerjanc J.: J. Chromatogr. A. 1169, 86–94 (2007)

    Article  CAS  Google Scholar 

  • Frobenius G.: Crelle’s J. 101, 273–299 (1887)

    Google Scholar 

  • A. Ryzhov et al (in preparation)

  • Harary F., Palmer E.: Am. Math. Soc. 17, 682–687 (1966)

    Article  Google Scholar 

  • Brown H., Hjelmeland L., Masinter L.: Discrete Math. 7, 1–30 (1974)

    Article  Google Scholar 

  • Brown H., Masinter L.: Discrete Math. 8, 227–244 (1974)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to D. J. Klein.

Additional information

An erratum to this article can be found at http://dx.doi.org/10.1007/s10910-008-9503-3

Rights and permissions

Reprints and permissions

About this article

Cite this article

Klein, D.J., Ryhzov, A. & Rosenfeld, V. Permutational isomers on a molecular skeleton with neighbor-excluding ligands. J Math Chem 45, 892–909 (2009). https://doi.org/10.1007/s10910-008-9461-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10910-008-9461-9

Keywords

Navigation