{"id":"https://openalex.org/W2788681089","doi":"https://doi.org/10.3934/mfc.2018003","title":"<i>L</i>(2, 1)-labeling of the Cartesian and strong product of two directed cycles","display_name":"<i>L</i>(2, 1)-labeling of the Cartesian and strong product of two directed cycles","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2788681089","doi":"https://doi.org/10.3934/mfc.2018003","mag":"2788681089"},"language":"en","primary_location":{"id":"doi:10.3934/mfc.2018003","is_oa":true,"landing_page_url":"https://doi.org/10.3934/mfc.2018003","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=5efa7de6-f446-4c85-a402-619b66f4cec7","source":{"id":"https://openalex.org/S4210238810","display_name":"Mathematical Foundations of Computing","issn_l":"2577-8838","issn":["2577-8838"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Foundations of Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.aimsciences.org/article/exportPdf?id=5efa7de6-f446-4c85-a402-619b66f4cec7","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012636371","display_name":"Zehui Shao","orcid":"https://orcid.org/0000-0003-0764-4135"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zehui Shao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032769891","display_name":"Huiqin Jiang","orcid":"https://orcid.org/0000-0002-3316-877X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huiqin Jiang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5058167920","display_name":"Aleksander Vesel","orcid":"https://orcid.org/0000-0003-3705-0071"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Aleksander Vesel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2619,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.5527523,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"1","issue":"1","first_page":"49","last_page":"61"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9725000262260437,"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/T10575","display_name":"Wireless Communication Networks Research","score":0.9697999954223633,"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":0.8308262825012207},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8248382806777954},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6684048175811768},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5535424947738647},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.44403076171875},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4142364263534546},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40966400504112244},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12013745307922363}],"concepts":[{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.8308262825012207},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8248382806777954},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6684048175811768},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5535424947738647},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.44403076171875},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4142364263534546},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40966400504112244},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12013745307922363},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3934/mfc.2018003","is_oa":true,"landing_page_url":"https://doi.org/10.3934/mfc.2018003","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=5efa7de6-f446-4c85-a402-619b66f4cec7","source":{"id":"https://openalex.org/S4210238810","display_name":"Mathematical Foundations of Computing","issn_l":"2577-8838","issn":["2577-8838"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Foundations of Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3934/mfc.2018003","is_oa":true,"landing_page_url":"https://doi.org/10.3934/mfc.2018003","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=5efa7de6-f446-4c85-a402-619b66f4cec7","source":{"id":"https://openalex.org/S4210238810","display_name":"Mathematical Foundations of Computing","issn_l":"2577-8838","issn":["2577-8838"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Foundations of Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2949097972","https://openalex.org/W2805104459","https://openalex.org/W2804776333","https://openalex.org/W4366733366","https://openalex.org/W3137798114","https://openalex.org/W4378087371","https://openalex.org/W2364608040","https://openalex.org/W2998748068","https://openalex.org/W1983442375","https://openalex.org/W3190844188"],"abstract_inverted_index":{"The":[0,104,120],"frequency":[1],"assignment":[2,7],"problem":[3],"(FAP)":[4],"is":[5,33,36,76,108,127,168,198],"the":[6,20,26,37,65,109,112,115,128,142,145,162,176,188,191],"of":[8,25,30,39,43,59,106,118,135,144,150,164,178,190,194],"frequencies":[9],"to":[10,16],"television":[11],"and":[12,57,69,95,114,147,171,185,201],"radio":[13],"transmitters":[14],"subject":[15],"restrictions":[17],"imposed":[18],"by":[19,125],"distance":[21,40,66],"between":[22,67,111,169,199],"transmitters.":[23],"One":[24],"graph":[27],"theoretical":[28],"models":[29],"FAP":[31],"which":[32],"well":[34],"elaborated":[35],"concept":[38],"constrained":[41],"labeling":[42],"graphs.":[44],"Let":[45],"$G":[46],"=":[47,93,102],"(V,":[48],"E)$":[49],"be":[50],"a":[51,77],"graph.":[52],"For":[53],"two":[54,151],"vertices":[55],"$u$":[56,68],"$v$":[58],"$G$,":[60,123],"we":[61,140],"denote":[62],"$d(u,":[63,91,100],"v)$":[64],"$v$.":[70],"An":[71],"$L(2,":[72,133],"1)$-labeling":[73],"for":[74,122,157,181,203],"$G$":[75],"function":[78],"$f:":[79],"V":[80],"\u2192":[81],"\\{0,":[82],"1,":[83],"\u00b7\u00b7\u00b7\\}$":[84],"such":[85],"that":[86,156,187],"$|f(u)-f(v)|":[87,96],"\u2265":[88,97,160,206],"1$":[89],"if":[90,99],"v)":[92,101],"2$":[94,98],"1$.":[103],"span":[105,130],"$f$":[107],"difference":[110],"largest":[113],"smallest":[116],"number":[117],"$f(V)$.":[119],"$\u03bb$-number":[121,143,163,177,189],"denoted":[124],"$\u03bb(G)$,":[126],"minimum":[129],"over":[131],"all":[132],"1)$-labelings":[134],"$G$.":[136],"In":[137],"this":[138],"paper,":[139],"study":[141],"Cartesian":[146],"strong":[148,192],"product":[149,193],"directed":[152],"cycles.":[153],"We":[154,173],"show":[155],"$m,":[158,204],"n":[159,205],"4$":[161],"$\\overrightarrow{C_m}":[165],"\\Box":[166],"\\overrightarrow{C_n}$":[167],"4":[170],"5.":[172],"also":[174],"establish":[175],"$\\overrightarrow{{{C}_{m}}}\\boxtimes":[179,196],"\\overrightarrow{{{C}_{n}}}$":[180,197],"$m":[182],"\u2264":[183],"10$":[184],"prove":[186],"cycles":[195],"6":[200],"8":[202],"48$.":[207]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}