PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 62 (76), pp. 112 (1997) 

Algebraic structure count of some cyclic hexagonalsquare chainsOlga BodrozaPanti]'cPrirodnoMatematicki fakultet, Novi Sad, YugoslaviaAbstract: Algebraic structure count ($ASC$value) of a bipartite graph $G$ is defined by $ASC\{G\} =\sqrt{\det A}$, where $A$ is the adjacency matrix of $G$. In the case of bipartite, plane graphs in which every faceboundary (cell) is a circuit of length $4s+2$ ($s=1,2,\ldots$), this number is equal to the number of the perfect matchings ($K$value) of $G$. However, if some of the circuits are of length $4s$ ($s=1,2,\ldots$), then the problem of evaluation of $ASC$value becomes more complicated. In this paper the algebraic structure count of the class of cyclic hexagonalsquare chains is determined. An explicit combinatorial formula for $ASC$ is deduced in the special case when all hexagonal fragments are isomorphic. Classification (MSC2000): 05C70; 05B50 Full text of the article:
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