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On identifying codes in partial linear spaces
dc.contributor.author | Araujo-Pardo, Gabriela |
dc.contributor.author | Montejano, Luis |
dc.contributor.author | Camino, Balbuena |
dc.contributor.author | Valenzuela, Juan Carlos |
dc.date.accessioned | 2011-05-05T07:44:03Z |
dc.date.available | 2011-05-05T07:44:03Z |
dc.date.issued | 2011 |
dc.identifier.citation | Araujo-Pardo, Gabriela [et al.]. On identifying codes in partial linear spaces. A: International Workshop on Optimal Networks Topologies. "Proceedings of the 3rd International Workshop on Optimal Networks Topologies IWONT 2010". 2011 ed. Barcelona: Iniciativa Digital Politècnica, 2011, p. 21-37. |
dc.identifier.isbn | 978-84-7653-565-3 |
dc.identifier.uri | http://hdl.handle.net/2099/10348 |
dc.description.abstract | Let (P,L, I) be a partial linear space and X ⊆ P ∪ L. Let us denote by (X)I = x∈X{y : yIx} and by [X] = (X)I ∪ X. With this terminology a partial linear space (P,L, I) is said to admit a (1,≤ k)-identifying code if the sets [X] are mutually different for all X ⊆ P ∪L with |X| ≤ k. In this paper we give a characterization of k-regular partial linear spaces admitting a (1,≤ k)-identifying code. Equivalently, we give a characterization of k-regular bipartite graphs of girth at least six admitting a (1,≤ k)-identifying code. That is, k-regular bipartite graphs of girth at least six admitting a set C of vertices such that the sets N[x] ∩ C are nonempty and pairwise distinct for all vertex x ∈ X where X is a subset of vertices of |X| ≤ k. Moreover, we present a family of k-regular partial linear spaces on 2(k−1)2+k points and 2(k − 1)2 + k lines whose incidence graphs do not admit a (1,≤ k)-identifying code. Finally, we show that the smallest (k; 6)-graphs known up to now for k − 1 not a prime power admit a (1,≤ k)-identifying code. |
dc.format.extent | 17 p. |
dc.language.iso | eng |
dc.publisher | Iniciativa Digital Politècnica |
dc.relation.ispartof | International Workshop on Optimal Networks Topologies |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs |
dc.subject.lcsh | Graph theory |
dc.subject.lcsh | Discrete geometry |
dc.title | On identifying codes in partial linear spaces |
dc.type | Conference report |
dc.subject.lemac | Grafs, Teoria de |
dc.subject.lemac | Geometria discreta |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::05 Combinatorics::05C Graph theory |
dc.rights.access | Open Access |
local.citation.author | Araujo-Pardo, Gabriela; Montejano, Luis; Camino, Balbuena; Valenzuela, Juan Carlos |
local.citation.contributor | International Workshop on Optimal Networks Topologies |
local.citation.pubplace | Barcelona |
local.citation.publicationName | Proceedings of the 3rd International Workshop on Optimal Networks Topologies IWONT 2010 |
local.citation.startingPage | 21 |
local.citation.endingPage | 37 |
local.citation.edition | 2011 |
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3er. 2010 [27]
Facultat de Matemàtiques i Estadística, Universitat Politècnica de Catalunya, Barcelona, 9-11 June 2010