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Incidence matrices of projective planes and of some regular bipartite graphs of girth 6 with few vertices
dc.contributor.author | Balbuena Martínez, Maria Camino Teófila |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III |
dc.date.accessioned | 2010-10-07T08:15:55Z |
dc.date.available | 2010-10-07T08:15:55Z |
dc.date.created | 2008-11 |
dc.date.issued | 2008-11 |
dc.identifier.citation | Balbuena, C. Incidence matrices of projective planes and of some regular bipartite graphs of girth 6 with few vertices. "SIAM journal on discrete mathematics", Novembre 2008, vol. 22, núm. 4, p. 1351-1363. |
dc.identifier.issn | 0895-4801 |
dc.identifier.uri | http://hdl.handle.net/2117/9495 |
dc.description.abstract | Let q be a prime power and r=0,1...,q−3. Using the Latin squares obtained by multiplying each entry of the addition table of the Galois field of order q by an element distinct from zero, we obtain the incidence matrices of projective planes and the incidence matrices of (q−r)-regular bipartite graphs of girth 6 and $q^2$−rq−1 vertices in each partite set. Moreover, in this work two Latin squares of order q−1 with entries belonging to {0,1,..., q}, not necessarily the same, are defined to be quasi row-disjoint if and only if the cartesian product of any two rows contains at most one pair (χ,χ) with χ≠0. Using these quasi row-disjoint Latin squares we find (q−1)-regular bipartite graphs of girth 6 with $q^2$−q−2 vertices in each partite set. Some of these graphs have the smallest number of vertices known so far among the regular graphs with girth 6. |
dc.format.extent | 13 p. |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs |
dc.subject.lcsh | Magic squares |
dc.subject.lcsh | Projective planes |
dc.subject.lcsh | Cages |
dc.subject.lcsh | Bipartite graphs |
dc.title | Incidence matrices of projective planes and of some regular bipartite graphs of girth 6 with few vertices |
dc.type | Article |
dc.subject.lemac | Quadrats màgics |
dc.subject.lemac | Geometria projectiva |
dc.subject.lemac | Bipartite graphs |
dc.subject.lemac | Grafs, Teoria de |
dc.contributor.group | Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions |
dc.identifier.doi | 10.1137/070688225 |
dc.relation.publisherversion | http://www-ma3.upc.es/users/balbuena/PAPERS/Girth6.pdf |
dc.rights.access | Open Access |
local.identifier.drac | 643514 |
dc.description.version | Postprint (published version) |
local.citation.author | Balbuena, C. |
local.citation.publicationName | SIAM journal on discrete mathematics |
local.citation.volume | 22 |
local.citation.number | 4 |
local.citation.startingPage | 1351 |
local.citation.endingPage | 1363 |
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