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dc.contributor.authorMiller, Mirka
dc.identifier.citationMiller, Mirka. An overview of the degree/diameter problem for directed, undirected and mixed graphs. A: International Workshop on Optimal Networks Topologies. "Proceedings of the 3rd International Workshop on Optimal Networks Topologies IWONT 2010". Barcelona: Iniciativa Digital Politècnica, 2011, p. 335-345.
dc.description.abstractA well-known fundamental problem in extremal graph theory is the degree/diameter problem, which is to determine the largest (in terms of the number of vertices) graphs or digraphs or mixed graphs of given maximum degree, respectively, maximum outdegree, respectively, mixed degree; and given diameter. General upper bounds, called Moore bounds, exist for the largest possible order of such graphs, digraphs and mixed graphs of given maximum degree d (respectively, maximum out-degree d, respectively, maximum mixed degree) and diameter k. In recent years, there have been many interesting new results in all these three versions of the problem, resulting in improvements in both the lower bounds and the upper bounds on the largest possible number of vertices. However, quite a number of questions regarding the degree/diameter problem are still wide open. In this paper we present an overview of the current state of the degree/diameter problem, for undirected, directed and mixed graphs, and we outline several related open problems.
dc.format.extent11 p.
dc.publisherIniciativa Digital Politècnica
dc.relation.ispartofInternational Workshop on Optimal Networks Topologies
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
dc.subject.lcshExtremal problems (Mathematics)
dc.subject.lcshGraph theory
dc.subject.lcshDirected graphs
dc.titleAn overview of the degree/diameter problem for directed, undirected and mixed graphs
dc.typeConference report
dc.subject.lemacProblemes extrems (Matemàtica)
dc.subject.lemacGrafs, Teoria de
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::05 Combinatorics::05D Extremal combinatorics
dc.subject.amsClassificació AMS::05 Combinatorics::05C Graph theory
dc.rights.accessOpen Access
upcommons.citation.authorMiller, Mirka
upcommons.citation.contributorInternational Workshop on Optimal Networks Topologies
upcommons.citation.publicationNameProceedings of the 3rd International Workshop on Optimal Networks Topologies IWONT 2010

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  • 3er. 2010 [27]
    Facultat de Matemàtiques i Estadística, Universitat Politècnica de Catalunya, Barcelona, 9-11 June 2010

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