Data di Pubblicazione:
2012
Citazione:
Totally unimodular nets / J.G. Eon, D.M. Proserpio, V.A. Blatov. - In: ACTA CRYSTALLOGRAPHICA. SECTION A, FOUNDATIONS OF CRYSTALLOGRAPHY. - ISSN 0108-7673. - 68:2(2012), pp. 286-294. [10.1107/S0108767312000062]
Abstract:
p-Periodic nets can be derived from a voltage graph G with voltages in Zp, the
free abelian group of rank p, if the cyclomatic number gamma of G is larger than p. Equivalently, one may describe a net by providing a set of (gamma - 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 subdeterminant
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.
Tipologia IRIS:
01 - Articolo su periodico
Elenco autori:
J.G. Eon, D.M. Proserpio, V.A. Blatov
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