Efficient edge domination in regular graphs

Bibliographic Details
Main Author: Cardoso, Domingos M.
Publication Date: 2008
Other Authors: Cerdeira, J.O., Delorme, Charles, Silva, Pedro C.
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10400.5/5615
Summary: An induced matching of a graph G is a matching having no two edges joined by an edge. An efficient edge dominating set of G is an induced matching M such that every other edge of G is adjacent to some edge in M. We relate maximum induced matchings and efficient edge dominating sets, showing that efficient edge dominating sets are maximum induced matchings, and that maximum induced matchings on regular graphs with efficient edge dominating sets are efficient edge dominating sets. A necessary condition for the existence of efficient edge dominating sets in terms of spectra of graphs is established. We also prove that, for arbitrary fixed p 3, deciding on the existence of efficient edge dominating sets on p-regular graphs is NP-complete
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spelling Efficient edge domination in regular graphsinduced matchingsdomination in graphsregular graphsNP-completenessAn induced matching of a graph G is a matching having no two edges joined by an edge. An efficient edge dominating set of G is an induced matching M such that every other edge of G is adjacent to some edge in M. We relate maximum induced matchings and efficient edge dominating sets, showing that efficient edge dominating sets are maximum induced matchings, and that maximum induced matchings on regular graphs with efficient edge dominating sets are efficient edge dominating sets. A necessary condition for the existence of efficient edge dominating sets in terms of spectra of graphs is established. We also prove that, for arbitrary fixed p 3, deciding on the existence of efficient edge dominating sets on p-regular graphs is NP-completeElsevierRepositório da Universidade de LisboaCardoso, Domingos M.Cerdeira, J.O.Delorme, CharlesSilva, Pedro C.2013-06-03T15:58:32Z20082008-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.5/5615eng"Discrete Applied Mathematics". ISSN 0166-218X. 156 (2008) 3060-30650166-218Xinfo:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2025-03-17T15:58:39Zoai:repositorio.ulisboa.pt:10400.5/5615Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-29T03:59:11.453592Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv Efficient edge domination in regular graphs
title Efficient edge domination in regular graphs
spellingShingle Efficient edge domination in regular graphs
Cardoso, Domingos M.
induced matchings
domination in graphs
regular graphs
NP-completeness
title_short Efficient edge domination in regular graphs
title_full Efficient edge domination in regular graphs
title_fullStr Efficient edge domination in regular graphs
title_full_unstemmed Efficient edge domination in regular graphs
title_sort Efficient edge domination in regular graphs
author Cardoso, Domingos M.
author_facet Cardoso, Domingos M.
Cerdeira, J.O.
Delorme, Charles
Silva, Pedro C.
author_role author
author2 Cerdeira, J.O.
Delorme, Charles
Silva, Pedro C.
author2_role author
author
author
dc.contributor.none.fl_str_mv Repositório da Universidade de Lisboa
dc.contributor.author.fl_str_mv Cardoso, Domingos M.
Cerdeira, J.O.
Delorme, Charles
Silva, Pedro C.
dc.subject.por.fl_str_mv induced matchings
domination in graphs
regular graphs
NP-completeness
topic induced matchings
domination in graphs
regular graphs
NP-completeness
description An induced matching of a graph G is a matching having no two edges joined by an edge. An efficient edge dominating set of G is an induced matching M such that every other edge of G is adjacent to some edge in M. We relate maximum induced matchings and efficient edge dominating sets, showing that efficient edge dominating sets are maximum induced matchings, and that maximum induced matchings on regular graphs with efficient edge dominating sets are efficient edge dominating sets. A necessary condition for the existence of efficient edge dominating sets in terms of spectra of graphs is established. We also prove that, for arbitrary fixed p 3, deciding on the existence of efficient edge dominating sets on p-regular graphs is NP-complete
publishDate 2008
dc.date.none.fl_str_mv 2008
2008-01-01T00:00:00Z
2013-06-03T15:58:32Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.5/5615
url http://hdl.handle.net/10400.5/5615
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv "Discrete Applied Mathematics". ISSN 0166-218X. 156 (2008) 3060-3065
0166-218X
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
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