{"id":"https://openalex.org/W4245806810","doi":"https://doi.org/10.1016/s0012-365x(99)90093-6","title":"A bound on the size of a graph with given order and bondage number","display_name":"A bound on the size of a graph with given order and bondage number","publication_year":1999,"publication_date":"1999-02-01","ids":{"openalex":"https://openalex.org/W4245806810","doi":"https://doi.org/10.1016/s0012-365x(99)90093-6"},"language":"en","primary_location":{"id":"doi:10.1016/s0012-365x(99)90093-6","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0012-365x(99)90093-6","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"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":"Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052665260","display_name":"Bert L. Hartnell","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bert L. Hartnell","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5073086838","display_name":"Douglas F. Rall","orcid":"https://orcid.org/0000-0002-5482-756X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Douglas F. Rall","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3000,"currency":"USD","value_usd":3000},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.42530294,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"197-198","issue":null,"first_page":"409","last_page":"413"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9990000128746033,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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":0.8761529922485352},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8304184079170227},{"id":"https://openalex.org/keywords/domination-analysis","display_name":"Domination analysis","score":0.7472166419029236},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6073470711708069},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6022998690605164},{"id":"https://openalex.org/keywords/bound-graph","display_name":"Bound graph","score":0.5187882781028748},{"id":"https://openalex.org/keywords/wheel-graph","display_name":"Wheel graph","score":0.512080729007721},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4854203164577484},{"id":"https://openalex.org/keywords/dominating-set","display_name":"Dominating set","score":0.45315951108932495},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4501103460788727},{"id":"https://openalex.org/keywords/path-graph","display_name":"Path graph","score":0.41794970631599426},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.4028375744819641},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.2111985981464386}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8761529922485352},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8304184079170227},{"id":"https://openalex.org/C83833204","wikidata":"https://www.wikidata.org/wiki/Q5290322","display_name":"Domination analysis","level":4,"score":0.7472166419029236},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6073470711708069},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6022998690605164},{"id":"https://openalex.org/C121134508","wikidata":"https://www.wikidata.org/wiki/Q4949882","display_name":"Bound graph","level":5,"score":0.5187882781028748},{"id":"https://openalex.org/C148364342","wikidata":"https://www.wikidata.org/wiki/Q948887","display_name":"Wheel graph","level":5,"score":0.512080729007721},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4854203164577484},{"id":"https://openalex.org/C146661039","wikidata":"https://www.wikidata.org/wiki/Q2915204","display_name":"Dominating set","level":4,"score":0.45315951108932495},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4501103460788727},{"id":"https://openalex.org/C128067373","wikidata":"https://www.wikidata.org/wiki/Q1415372","display_name":"Path graph","level":5,"score":0.41794970631599426},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.4028375744819641},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.2111985981464386},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0012-365x(99)90093-6","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0012-365x(99)90093-6","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"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":"Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.49000000953674316,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1989623169","https://openalex.org/W1993155410","https://openalex.org/W2001321001","https://openalex.org/W2040414111","https://openalex.org/W2041387840","https://openalex.org/W2078824348","https://openalex.org/W2257654414","https://openalex.org/W2753014556","https://openalex.org/W6692269798","https://openalex.org/W6743981021"],"related_works":["https://openalex.org/W4298388358","https://openalex.org/W1995383828","https://openalex.org/W4288436438","https://openalex.org/W2077631478","https://openalex.org/W4242930043","https://openalex.org/W1970462054","https://openalex.org/W2090130267","https://openalex.org/W2004791814","https://openalex.org/W2161439427","https://openalex.org/W4246526124"],"abstract_inverted_index":null,"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}