Totally unimodular nets.
Acta Crystallogr A
; 68(Pt 2): 286-94, 2012 Mar.
Article
em En
| MEDLINE
| ID: mdl-22338663
p-Periodic nets can be derived from a voltage graph G with voltages in Z(p), the free abelian group of rank p, if the cyclomatic number γ of G is larger than p. Equivalently, one may describe a net by providing a set of (γ - p) cycle vectors of G forming a basis of the subspace of the cycle space of G with zero net voltage. Let M be the matrix of this basis expressed in the edge basis of the 1-chain space of G. A net is called totally unimodular whenever every sub-determinant of M belongs to the set {-1, 0, 1}. Only a finite set of totally unimodular nets can be derived from some finite graph. It is shown that totally unimodular nets are stable under the operation of edge-lattice deletion in a sense that makes them comparable to minimal nets. An algorithm for the complete determination of totally unimodular nets derived from some finite graph is presented. As an application, the full list of totally unimodular nets derived from graphs of cyclomatic numbers 3 and 4, without bridges, is given. It is shown that many totally unimodular nets frequently occur in crystal structures.
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Base de dados:
MEDLINE
Idioma:
En
Revista:
Acta Crystallogr A
Ano de publicação:
2012
Tipo de documento:
Article
País de afiliação:
Brasil
País de publicação:
Estados Unidos