{"id":"https://openalex.org/W4405114664","doi":"https://doi.org/10.1515/math-2024-0097","title":"On k -prime graphs","display_name":"On k -prime graphs","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4405114664","doi":"https://doi.org/10.1515/math-2024-0097"},"language":"en","primary_location":{"id":"doi:10.1515/math-2024-0097","doi":"https://doi.org/10.1515/math-2024-0097","is_oa":true,"landing_page_url":"https://doi.org/10.1515/math-2024-0097","pdf_url":"https://www.degruyterbrill.com/document/doi/10.1515/math-2024-0097/pdf","source":{"id":"https://openalex.org/S44620559","display_name":"Open Mathematics","issn_l":"1644-3616","issn":["1644-3616","1895-1074","2391-5455"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","dongbi-d","jufo-1","norway-1","oarl","poland-40","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Open Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.degruyterbrill.com/document/doi/10.1515/math-2024-0097/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030079374","display_name":"Omar A. AbuGhneim","orcid":"https://orcid.org/0000-0001-9080-0260","observed_orcids":["https://orcid.org/0000-0001-9080-0260"]},"institutions":[{"id":"https://openalex.org/I114972647","display_name":"University of Jordan","ror":"https://ror.org/05k89ew48","country_code":"JO","type":"education","lineage":["https://openalex.org/I114972647"]}],"countries":["JO"],"is_corresponding":true,"raw_author_name":"Omar A. Abughneim","raw_affiliation_strings":["Department of Mathematics, The University of Jordan , Amman , Jordan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The University of Jordan , Amman , Jordan","institution_ids":["https://openalex.org/I114972647"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088620525","display_name":"Baha\u2019 Abughazaleh","orcid":"https://orcid.org/0000-0002-7188-9180","observed_orcids":["https://orcid.org/0000-0002-7188-9180"]},"institutions":[{"id":"https://openalex.org/I92449659","display_name":"Isra University","ror":"https://ror.org/04d4bt482","country_code":"JO","type":"education","lineage":["https://openalex.org/I92449659"]}],"countries":["JO"],"is_corresponding":false,"raw_author_name":"Baha\u2019 Abughazaleh","raw_affiliation_strings":["Department of Mathematics, Isra University , Amman , Jordan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Isra University , Amman , Jordan","institution_ids":["https://openalex.org/I92449659"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5030079374"],"corresponding_institution_ids":["https://openalex.org/I114972647"],"apc_list":{"value":1000,"currency":"EUR","value_usd":1082},"apc_paid":{"value":1000,"currency":"EUR","value_usd":1082},"fwci":0.5215,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.54102931,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"22","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9994999766349792,"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":0.9994999766349792,"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":0.00019999999494757503,"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/T14500","display_name":"Smarandache Functions and Recreational Number Theory","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/graph-labeling","display_name":"graph labeling","score":0.7360000014305115},{"id":"https://openalex.org/keywords/independence-number","display_name":"independence number","score":0.5979999899864197},{"id":"https://openalex.org/keywords/cycles","display_name":"cycles","score":0.8029999732971191},{"id":"https://openalex.org/keywords/small-graphs","display_name":"small graphs","score":0.4749999940395355}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8424293994903564},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5987038016319275},{"id":"https://openalex.org/C169654258","wikidata":"https://www.wikidata.org/wiki/Q12479","display_name":"Number theory","level":2,"score":0.5754197835922241},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5115271806716919},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40853992104530334}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1515/math-2024-0097","doi":"https://doi.org/10.1515/math-2024-0097","is_oa":true,"landing_page_url":"https://doi.org/10.1515/math-2024-0097","pdf_url":"https://www.degruyterbrill.com/document/doi/10.1515/math-2024-0097/pdf","source":{"id":"https://openalex.org/S44620559","display_name":"Open Mathematics","issn_l":"1644-3616","issn":["1644-3616","1895-1074","2391-5455"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","dongbi-d","jufo-1","norway-1","oarl","poland-40","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Open Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:3178320beb4341d7a5ade9b4940d11fa","doi":null,"is_oa":false,"landing_page_url":"https://doaj.org/article/3178320beb4341d7a5ade9b4940d11fa","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"Open Mathematics, Vol 22, Iss 1, Pp 365-3566 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1515/math-2024-0097","doi":"https://doi.org/10.1515/math-2024-0097","is_oa":true,"landing_page_url":"https://doi.org/10.1515/math-2024-0097","pdf_url":"https://www.degruyterbrill.com/document/doi/10.1515/math-2024-0097/pdf","source":{"id":"https://openalex.org/S44620559","display_name":"Open Mathematics","issn_l":"1644-3616","issn":["1644-3616","1895-1074","2391-5455"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","dongbi-d","jufo-1","norway-1","oarl","poland-40","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Open Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4405114664.pdf","grobid_xml":"https://content.openalex.org/works/W4405114664.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W1979302699","https://openalex.org/W1988315105","https://openalex.org/W2013161318","https://openalex.org/W2965911612","https://openalex.org/W4214880424","https://openalex.org/W4240651097","https://openalex.org/W4390603808","https://openalex.org/W4403934313"],"related_works":["https://openalex.org/W7097508694","https://openalex.org/W2965911612","https://openalex.org/W6907767930","https://openalex.org/W4385615583","https://openalex.org/W6920163534","https://openalex.org/W4408095257","https://openalex.org/W4289943647","https://openalex.org/W7221010157","https://openalex.org/W3036823652","https://openalex.org/W7061393681"],"abstract_inverted_index":{"Abstract":[0],"In":[1,93],"the":[2,23,141],"context":[3],"of":[4,114,144],"a":[5,12,74,85,99,106,112,118,137,145,152,155],"simple":[6],"undirected":[7],"graph":[8,89,100,113],"G":[9,10,37,57,58,71,72,82,83],",":[11,27,31,33],"k":[13,14,26,28,41,75,76,86,87,91,107,119,122,123,125,146,156],"-prime":[15,77,88],"labeling":[16],"refers":[17],"to":[18,49,67,102],"assigning":[19],"distinct":[20],"integers":[21],"from":[22],"set":[24],"{":[25],"+":[29,40,126],"1":[30,43,127],"\u2026":[32],"\u2223":[34,39],"V":[35],"(":[36,90],")":[38],"\u2212":[42],"}":[44],"\\left\\{k,k+1,\\ldots":[45],",|":[46],"V\\left(G)|":[47],"+k-1\\right\\}":[48],"its":[50],"vertices,":[51],"such":[52],"that":[53,63,81],"adjacent":[54],"vertices":[55],"in":[56],"are":[59,64,129],"labeled":[60],"with":[61],"numbers":[62],"relatively":[65],"prime":[66],"each":[68],"other.":[69],"If":[70],"has":[73],"labeling,":[78],"we":[79,96,135,149],"say":[80],"is":[84,105,117,154],"-PG).":[92],"this":[94],"article,":[95],"characterize":[97,110],"when":[98,111,151],"up":[101],"order":[103,115],"6":[104],"-PG":[108,120],"and":[109,124],"7":[116],"whenever":[121],"k+1":[128],"not":[130],"divisible":[131],"by":[132],"5.":[133],"Also,":[134],"find":[136],"lower":[138],"bound":[139],"for":[140],"independence":[142],"number":[143],"-PG.":[147,157],"Finally,":[148],"study":[150],"cycle":[153]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2024-12-07T00:00:00"}