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



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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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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