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On congruence in $Z^n$ and the dimension of a multidimensional circulant
dc.contributor.author | Fiol Mora, Miquel Àngel |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV |
dc.date.accessioned | 2008-08-01T12:53:49Z |
dc.date.available | 2008-08-01T12:53:49Z |
dc.date.created | 1995 |
dc.date.issued | 1995 |
dc.identifier.citation | Fiol 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.uri | http://hdl.handle.net/2117/2200 |
dc.description.abstract | From 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.extent | 15 p. |
dc.language.iso | eng |
dc.publisher | Elsevier |
dc.subject.lcsh | Graph theory |
dc.subject.other | Congruence in $Z^n$ |
dc.subject.other | Multidimensional circulant |
dc.subject.other | Cayley digraph |
dc.subject.other | Cartesian product |
dc.subject.other | Smith normal form |
dc.subject.other | Cyclic group |
dc.title | On congruence in $Z^n$ and the dimension of a multidimensional circulant |
dc.type | Article |
dc.subject.lemac | Grafs, Teoria de |
dc.contributor.group | Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::05 Combinatorics::05C Graph theory |
dc.rights.access | Open Access |
local.personalitzacitacio | true |
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