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dc.contributor.authorFiol Mora, Miquel Àngel
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV
dc.date.accessioned2008-08-01T12:53:49Z
dc.date.available2008-08-01T12:53:49Z
dc.date.created1995
dc.date.issued1995
dc.identifier.citationFiol Mora, Miquel Àngel. "On congruence in $Z^n$ and the dimension of a multidimensional circulant". Discrete Mathematics, 1995, vol. 141, núm. 1-3, p. 123-134.
dc.identifier.urihttp://hdl.handle.net/2117/2200
dc.description.abstractFrom a generalization to $Z^n$ of the concept of congruence we define a family of regular digraphs or graphs called multidimensional circulants, which turn to be Cayley (di)graphs of Abelian groups. This paper is mainly devoted to show the relationship between the Smith normal form for integral matrices and the dimension of such (di)graphs, that is the minimum ranks of the groups they can arise from. In particular, those 2-step multidimensional circulant which are circulants, that is Cayley (di)graphs of cyclic groups, are fully characterized. In addition, a reasoning due to Lawrence is used to prove that the cartesian product of $n$ circulants with equal number of vertice $p>2$, $p$ a prime, has dimension $n$.
dc.format.extent15 p.
dc.language.isoeng
dc.publisherElsevier
dc.subject.lcshGraph theory
dc.subject.otherCongruence in $Z^n$
dc.subject.otherMultidimensional circulant
dc.subject.otherCayley digraph
dc.subject.otherCartesian product
dc.subject.otherSmith normal form
dc.subject.otherCyclic group
dc.titleOn congruence in $Z^n$ and the dimension of a multidimensional circulant
dc.typeArticle
dc.subject.lemacGrafs, Teoria de
dc.contributor.groupUniversitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::05 Combinatorics::05C Graph theory
dc.rights.accessOpen Access
local.personalitzacitaciotrue


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