Journal of Mathematical Chemistry

, Volume 41, Issue 3, pp 283–294 | Cite as

Algebraic Structure Count of Some Cyclic Hexagonal-Square Chains on the Möbius Strip

  • Olga Bodroža-Pantić


The concept of ASC (Algebraic structure count) is introduced into theoretical organic chemistry by Wilcox as the difference between the number of so-called “even” and “odd” Kekulé structures of a conjugated molecule. Precisely, algebraic structure count (ASC-value) of the bipartite graph G corresponding to the skeleton of a conjugated hydrocarbon is defined by \({\rm ASC} \{G \} \mathop{=}\limits^{\rm def} \sqrt{\mid {\rm det} A \mid}\) where A is the adjacency matrix of G. The determination of algebraic structure count of (bipartite) cyclic hexagonal-square chains in the the class of plane such graphs is known. In this paper we expand these considerations on the non-plane class. An explicit combinatorial formula for ASC is deduced in the special case when all hexagonal fragments are isomorphic.


algebraic structure count Kekulé structure 

AMS subject classification (2001)

05C70 05C50 05B50 05A15 


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  1. 1.
    Wilcox C.F. (1968). Tetrahedron Lett 7:795CrossRefGoogle Scholar
  2. 2.
    Wilcox C.F. (1969). J. Am. chem. Soc 91:2732CrossRefGoogle Scholar
  3. 3.
    Dewar M.J.S. and Longuet-Higgins H.C. (1952). Proc. Roy. Soc. London A214:482CrossRefGoogle Scholar
  4. 4.
    Gutman I., Trinajstić N., Wilcox C.F. (1975). Tetrahedron 31:143CrossRefGoogle Scholar
  5. 5.
    Wilcox C.F., Gutman I., Trinajstić N. (1975). Tetrahedron 31:147CrossRefGoogle Scholar
  6. 6.
    Trinajstić N. (1992). Chemical Graph Theory. CRC Press, Boca RatonGoogle Scholar
  7. 7.
    Gutman I., Cyvin S.J. (1989). Introduction to the theory of benzenoid hydrocarbons. Springer, BerlinGoogle Scholar
  8. 8.
    Cvetković D.M., Doob M., Sachs H. (1982). Spectra of Graphs. VEB Deutscher Verlag der Wissenschaften, BerlinGoogle Scholar
  9. 9.
    Cyvin S.J., and Gutman I. (1988). Kekulé Structures in Benzenoid Hydrocarbons. Lecture Notes in Chemistry 46 Springer-Verlag, BerlinGoogle Scholar
  10. 10.
    Gutman I. (1984). Z. Naturforsch. 39a:794Google Scholar
  11. 11.
    Gutman I. (1993). Indian J. Chem 32A:281Google Scholar
  12. 12.
    Gutman I. (1993). J. Chem. Soc. Faraday Trans. 89:2413CrossRefGoogle Scholar
  13. 13.
    Cyvin S.J., Gutman I., Bodroža-Pantić O., Brunvoll J. (1994). Acta. Chim. Hung (Models in Chemistry) 131(6):777Google Scholar
  14. 14.
    Bodroža-Pantić O., Cyvin S.J., and Gutman I. (1995). Commun. Math. Chem (MATCH) 32:47Google Scholar
  15. 15.
    Bodroža-Pantić O., Gutman I., Cyvin S.J. (1996). Acta Chim. Hung. (Models in Chemistry) 133:27Google Scholar
  16. 16.
    Bodroža-Pantić O. (1997). Publications De L’Institut Mathématique 62(76):1Google Scholar
  17. 17.
    Babić D., Graovac A., Gutman I. (1995). Polycyclic Aromatic Compoundes 4:199Google Scholar
  18. 18.
    Bodroža-Pantić O., Doroslovački R. (2004). J. Math. Chem 35(2):139CrossRefGoogle Scholar
  19. 19.
    Bodroža-Pantić O., Gutman I., Cyvin S.J. (1997). Fibonacci Quart 35(1):75Google Scholar
  20. 20.
    Tošić R., Bodroža O. (1991). Fibonacci Quart 29(1):7Google Scholar
  21. 21.
    Tošić R., Bodroža O. (1989). Commun Math. Chem. (MATCH) 24:311Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Department of Mathematics and InformaticsUniversity of Novi SadNovi SadSerbia

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