{"id":"https://openalex.org/W1982894246","doi":"https://doi.org/10.1016/j.aml.2008.02.012","title":"Defensive <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si1.gif\" display=\"inline\" overflow=\"scroll\"><mml:mi>k</mml:mi></mml:math>-alliances in graphs","display_name":"Defensive <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si1.gif\" display=\"inline\" overflow=\"scroll\"><mml:mi>k</mml:mi></mml:math>-alliances in graphs","publication_year":2008,"publication_date":"2008-03-31","ids":{"openalex":"https://openalex.org/W1982894246","doi":"https://doi.org/10.1016/j.aml.2008.02.012","mag":"1982894246"},"language":"en","primary_location":{"id":"doi:10.1016/j.aml.2008.02.012","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.aml.2008.02.012","pdf_url":null,"source":{"id":"https://openalex.org/S7571225","display_name":"Applied Mathematics Letters","issn_l":"0893-9659","issn":["0893-9659","1873-5452"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics Letters","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/math/0611180","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066088171","display_name":"Juan A. Rodr\u00edguez\u2010Vel\u00e1zquez","orcid":"https://orcid.org/0000-0002-9082-7647"},"institutions":[{"id":"https://openalex.org/I55952717","display_name":"Universitat Rovira i Virgili","ror":"https://ror.org/00g5sqv46","country_code":"ES","type":"education","lineage":["https://openalex.org/I55952717"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Juan A. Rodr\u00edguez-Vel\u00e1zquez","raw_affiliation_strings":["Department of Computer Engineering and Mathematics, Rovira i Virgili University of Tarragona, Av. Pa\u00efsos Catalans 26, 43007 Tarragona, Spain","Department of Computer Engineering and Mathematics, Rovira i Virgili University of Tarragona, Av. Pa\u00efsos Catalans 26, 43007 Tarragona, Spain#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Computer Engineering and Mathematics, Rovira i Virgili University of Tarragona, Av. Pa\u00efsos Catalans 26, 43007 Tarragona, Spain","institution_ids":["https://openalex.org/I55952717"]},{"raw_affiliation_string":"Department of Computer Engineering and Mathematics, Rovira i Virgili University of Tarragona, Av. Pa\u00efsos Catalans 26, 43007 Tarragona, Spain#TAB#","institution_ids":["https://openalex.org/I55952717"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088195854","display_name":"Ismael G. Yero","orcid":"https://orcid.org/0000-0002-1619-1572"},"institutions":[{"id":"https://openalex.org/I55952717","display_name":"Universitat Rovira i Virgili","ror":"https://ror.org/00g5sqv46","country_code":"ES","type":"education","lineage":["https://openalex.org/I55952717"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Ismael G. Yero","raw_affiliation_strings":["Department of Computer Engineering and Mathematics, Rovira i Virgili University of Tarragona, Av. Pa\u00efsos Catalans 26, 43007 Tarragona, Spain","Department of Computer Engineering and Mathematics, Rovira i Virgili University of Tarragona, Av. Pa\u00efsos Catalans 26, 43007 Tarragona, Spain#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Computer Engineering and Mathematics, Rovira i Virgili University of Tarragona, Av. Pa\u00efsos Catalans 26, 43007 Tarragona, Spain","institution_ids":["https://openalex.org/I55952717"]},{"raw_affiliation_string":"Department of Computer Engineering and Mathematics, Rovira i Virgili University of Tarragona, Av. Pa\u00efsos Catalans 26, 43007 Tarragona, Spain#TAB#","institution_ids":["https://openalex.org/I55952717"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041892602","display_name":"Jos\u00e9 M. Sigarreta","orcid":"https://orcid.org/0000-0002-0863-4695"},"institutions":[{"id":"https://openalex.org/I50357001","display_name":"Universidad Carlos III de Madrid","ror":"https://ror.org/03ths8210","country_code":"ES","type":"education","lineage":["https://openalex.org/I50357001"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Jos\u00e9 M. Sigarreta","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Legan\u00e9s (Madrid), Spain","Departamento de Matem\u00e1ticas, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Legan\u00e9s-Madrid, Spain#TAB#"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Legan\u00e9s (Madrid), Spain","institution_ids":["https://openalex.org/I50357001"]},{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Legan\u00e9s-Madrid, Spain#TAB#","institution_ids":["https://openalex.org/I50357001"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5066088171"],"corresponding_institution_ids":["https://openalex.org/I55952717"],"apc_list":{"value":3540,"currency":"USD","value_usd":3540},"apc_paid":null,"fwci":4.9614,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.948604,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"22","issue":"1","first_page":"96","last_page":"100"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7922874689102173},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7480196952819824},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6347215175628662},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5712189674377441},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.5710974931716919},{"id":"https://openalex.org/keywords/simple-graph","display_name":"Simple graph","score":0.5025222301483154},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.41383570432662964},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33223995566368103}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7922874689102173},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7480196952819824},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6347215175628662},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5712189674377441},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.5710974931716919},{"id":"https://openalex.org/C2993105083","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Simple graph","level":3,"score":0.5025222301483154},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.41383570432662964},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33223995566368103},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1016/j.aml.2008.02.012","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.aml.2008.02.012","pdf_url":null,"source":{"id":"https://openalex.org/S7571225","display_name":"Applied Mathematics Letters","issn_l":"0893-9659","issn":["0893-9659","1873-5452"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics Letters","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:math/0611180","is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0611180","pdf_url":"https://arxiv.org/pdf/math/0611180","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:math/0611180","is_oa":true,"landing_page_url":"http://arxiv.org/abs/math/0611180","pdf_url":"https://arxiv.org/pdf/math/0611180","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W124491349","https://openalex.org/W1565752646","https://openalex.org/W1589331344","https://openalex.org/W1925349455","https://openalex.org/W1984374364","https://openalex.org/W1987326317","https://openalex.org/W2005870236","https://openalex.org/W2019684082","https://openalex.org/W2040495536","https://openalex.org/W2095078730","https://openalex.org/W2107940287","https://openalex.org/W2132088887","https://openalex.org/W2151417892","https://openalex.org/W4295678724","https://openalex.org/W6842435522"],"related_works":["https://openalex.org/W4310825608","https://openalex.org/W2897806428","https://openalex.org/W2078517125","https://openalex.org/W2391518723","https://openalex.org/W2805115653","https://openalex.org/W1996149838","https://openalex.org/W4205475737","https://openalex.org/W2364012696","https://openalex.org/W2622512907","https://openalex.org/W4312839729"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-28T08:17:26.163206","created_date":"2016-06-24T00:00:00"}