Skip to main content
SpringerLink
Log in

The Unfixed Subgraph of a Catacondensed Hexagonal System Obtained by Fixing an Alternating Set

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

Abstract

We show that the unfixed subgraph of a catacondensed hexagonal system obtained by fixing an alternating set is either empty or its components are catacondensed hexagonal systems. Also, we provide some alternating sets for which this unfixed subgraph is empty. Finally, we prove that, in catacondensed hexagonal systems, the concept of a maximal M-resonant set, where M is a perfect matching, is equivalent to that of a maximal resonant set

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. I. Gutman S.J. Cyvin (1989) Introduction to the Theory of Benzenoid Hydrocarbons Springer-Verlag Berlin

    Google Scholar 

  2. N. Ohkami A. Motoyama T. Yamaguchi H. Hosoya I. Gutman (1981) Tetrahedron 37 1113 Occurrence Handle10.1016/S0040-4020(01)92040-X

    Article  Google Scholar 

  3. Abeledo H., Atkinson G. in: Discrete Mathematical Chemistry, eds. P. Hansen, P. Fowler and M. Zheng (Am. Math. Soc., Providence, RI, 2000), pp. 1–8.

  4. I. Gutman (1983) Wiss. Z. Thechn. Hochsch. Ilmenau 29 57

    Google Scholar 

  5. M. Randić (1976) J. Chem. Soc 72 232

    Google Scholar 

  6. P. Hansen M. Zheng (1994) J. Chem. Inf. Comput. Sci 39 297 Occurrence Handle10.1021/ci00018a011

    Article  Google Scholar 

  7. I. Gutman H. Hosoya T. Yamaguchi A. Motoyama N. Kuboi (1977) Bull Soc. Chim. Beograd 42 503

    Google Scholar 

  8. I. Gutman (1982) MATCH Commun. Math. Chem 13 173

    Google Scholar 

  9. Gutman I. Proceedings of the Fourth Yugoslav Seminar on Graph Theory, Novi Sad: Institute of Mathematics, University of Novi Sad (1983) 151.

  10. Salem K. Alternating sets and resonant sets of a hexagonal system, DSc dissertation, The George Washington University, USA, in preparation.

Download references

Author information

Author notes

  1. Khaled Salem

    Present address: Khaled Salem, 66 Youssef Abbas Street, Apt. 71, Cairo, Nasr City, Postal Code 11371, Egypt

Authors and Affiliations

  1. Department of Engineering Management & Systems Engineering, The George Washington University, Washington, D.C, 20052, USA

    Khaled Salem

  2. Faculty of Science, University of Kragujevac, P.O. Box 60, 34000, Kragujevac, Serbia & Montenegro

    Ivan Gutman

Authors
  1. Khaled Salem
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ivan Gutman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Khaled Salem.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Salem, K., Gutman, I. The Unfixed Subgraph of a Catacondensed Hexagonal System Obtained by Fixing an Alternating Set. J Math Chem 38, 503–510 (2005). https://doi.org/10.1007/s10910-004-6896-5

Download citation

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10910-004-6896-5

Keywords

AMS subject classification

Search

Navigation