Geodesic
Algebraic Structure Count of Some Cyclic Hexagonal-square Chains
Publications de l'Institut Mathématique, _N_S_62 (1997) no. 76, p. 1 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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 face-boundary (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 hexagonal-square chains is determined. An explicit combinatorial formula for $ASC$ is deduced in the special case when all hexagonal fragments are isomorphic.
Classification : 05C70 05B50 
@article{PIM_1997_N_S_62_76_a0,
     author = {Olga Bodro\v{z}a-Panti\'c},
     title = {Algebraic {Structure} {Count} of {Some} {Cyclic} {Hexagonal-square} {Chains}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {1 },
     publisher = {mathdoc},
     volume = {_N_S_62},
     number = {76},
     year = {1997},
     zbl = {0942.05053},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1997_N_S_62_76_a0/}
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Olga Bodroža-Pantić. Algebraic Structure Count of Some Cyclic Hexagonal-square Chains. Publications de l'Institut Mathématique, _N_S_62 (1997) no. 76, p. 1 . http://geodesic.mathdoc.fr/item/PIM_1997_N_S_62_76_a0/