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.
@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/}
}
TY - JOUR AU - Olga Bodroža-Pantić TI - Algebraic Structure Count of Some Cyclic Hexagonal-square Chains JO - Publications de l'Institut Mathématique PY - 1997 SP - 1 VL - _N_S_62 IS - 76 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/PIM_1997_N_S_62_76_a0/ LA - en ID - PIM_1997_N_S_62_76_a0 ER -
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/