{"id":"https://openalex.org/W2131784590","doi":"https://doi.org/10.1142/s1793830914500335","title":"The decycling number of $P_{m} \\square P_{n}^{\\ast}$","display_name":"The decycling number of $P_{m} \\square P_{n}^{\\ast}$","publication_year":2014,"publication_date":"2014-02-20","ids":{"openalex":"https://openalex.org/W2131784590","doi":"https://doi.org/10.1142/s1793830914500335","mag":"2131784590"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830914500335","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830914500335","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","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/A5045066989","display_name":"Min-Yun Lien","orcid":null},"institutions":[{"id":"https://openalex.org/I148366613","display_name":"National Yang Ming Chiao Tung University","ror":"https://ror.org/00se2k293","country_code":"TW","type":"education","lineage":["https://openalex.org/I148366613"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Min-Yun Lien","raw_affiliation_strings":["Department of Applied Mathematics, National Chiao Tung University, Hsinchu, 30010, Taiwan"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, National Chiao Tung University, Hsinchu, 30010, Taiwan","institution_ids":["https://openalex.org/I148366613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008893362","display_name":"Hung\u2010Lin Fu","orcid":"https://orcid.org/0000-0001-7218-3043"},"institutions":[{"id":"https://openalex.org/I148366613","display_name":"National Yang Ming Chiao Tung University","ror":"https://ror.org/00se2k293","country_code":"TW","type":"education","lineage":["https://openalex.org/I148366613"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Hung-Lin Fu","raw_affiliation_strings":["Department of Applied Mathematics, National Chiao Tung University, Hsinchu, 30010, Taiwan"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, National Chiao Tung University, Hsinchu, 30010, Taiwan","institution_ids":["https://openalex.org/I148366613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008333729","display_name":"Chie-Huai Shih","orcid":null},"institutions":[{"id":"https://openalex.org/I148366613","display_name":"National Yang Ming Chiao Tung University","ror":"https://ror.org/00se2k293","country_code":"TW","type":"education","lineage":["https://openalex.org/I148366613"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Chie-Huai Shih","raw_affiliation_strings":["Department of Applied Mathematics, National Chiao Tung University, Hsinchu, 30010, Taiwan"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, National Chiao Tung University, Hsinchu, 30010, Taiwan","institution_ids":["https://openalex.org/I148366613"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5045066989"],"corresponding_institution_ids":["https://openalex.org/I148366613"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.15416278,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"06","issue":"03","first_page":"1450033","last_page":"1450033"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9936000108718872,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9936000108718872,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9919000267982483,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9898999929428101,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cartesian-product","display_name":"Cartesian product","score":0.8392125368118286},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8218249678611755},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7644162178039551},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.7002826929092407},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6662253737449646},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46945470571517944}],"concepts":[{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.8392125368118286},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8218249678611755},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7644162178039551},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.7002826929092407},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6662253737449646},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46945470571517944}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830914500335","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830914500335","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1575434249","https://openalex.org/W1975145864","https://openalex.org/W1978731130","https://openalex.org/W1985300267","https://openalex.org/W1995044685","https://openalex.org/W2000338110","https://openalex.org/W2002052439","https://openalex.org/W2043414428","https://openalex.org/W2089749235","https://openalex.org/W2124463034","https://openalex.org/W3141776272","https://openalex.org/W4240625092","https://openalex.org/W4245562137","https://openalex.org/W4253960404","https://openalex.org/W4254703335"],"related_works":["https://openalex.org/W2070252991","https://openalex.org/W2807449856","https://openalex.org/W4366733366","https://openalex.org/W3137798114","https://openalex.org/W2172011430","https://openalex.org/W4378087371","https://openalex.org/W2364608040","https://openalex.org/W2998748068","https://openalex.org/W1983442375","https://openalex.org/W3190844188"],"abstract_inverted_index":{"A":[0],"set":[1,17,27],"of":[2,4,18,24,28,39,52,56,82,93],"vertices":[3],"a":[5,15,25,29],"graph":[6,12,30],"whose":[7],"removal":[8],"leaves":[9],"an":[10],"acyclic":[11],"is":[13,32],"called":[14],"decycling":[16,26,37,50],"the":[19,36,49,53,79],"graph.":[20],"The":[21],"minimum":[22],"size":[23],"G":[31],"referred":[33],"to":[34],"as":[35],"number":[38,51],"G,":[40],"denoted":[41],"by":[42],"\u2207(G).":[43],"In":[44],"this":[45],"paper,":[46],"we":[47,70,77],"study":[48],"Cartesian":[54],"product":[55],"two":[57],"paths,":[58],"\u2207(P":[59,83],"m":[60,84],"\u25a1P":[61,85],"n":[62,86],"),":[63],"and":[64],"obtain":[65,78],"several":[66],"new":[67],"results.":[68],"Mainly,":[69],"prove":[71],"that":[72],"[Formula:":[73],"see":[74],"text].":[75],"Moreover,":[76],"exact":[80],"value":[81],")":[87],"for":[88],"some":[89],"classes":[90],"(modulo":[91],"6)":[92],"pairs":[94],"(m,":[95],"n).":[96]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}