{"id":"https://openalex.org/W3034758533","doi":"https://doi.org/10.1109/access.2020.3002397","title":"Radio Labeling for Strong Product K<sub>3</sub> \u22a0 P<sub>n</sub>","display_name":"Radio Labeling for Strong Product K<sub>3</sub> \u22a0 P<sub>n</sub>","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3034758533","doi":"https://doi.org/10.1109/access.2020.3002397","mag":"3034758533"},"language":"en","primary_location":{"id":"doi:10.1109/access.2020.3002397","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.3002397","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/09116989.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/09116989.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018970039","display_name":"Hengxiao Qi","orcid":"https://orcid.org/0000-0003-0911-7523"},"institutions":[{"id":"https://openalex.org/I2800350601","display_name":"Central Committee of the Communist Party of China","ror":"https://ror.org/00akhyy70","country_code":"CN","type":"government","lineage":["https://openalex.org/I2800350601"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hengxiao Qi","raw_affiliation_strings":["Party School of Shandong Provincial Committee of the Communist Party of China, Shandong Administration College, Jinan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Party School of Shandong Provincial Committee of the Communist Party of China, Shandong Administration College, Jinan, China","institution_ids":["https://openalex.org/I2800350601"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027421648","display_name":"Saima Nazeer","orcid":"https://orcid.org/0000-0003-2792-1670"},"institutions":[{"id":"https://openalex.org/I161237661","display_name":"Lahore College for Women University","ror":"https://ror.org/02bf6br77","country_code":"PK","type":"education","lineage":["https://openalex.org/I161237661"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Saima Nazeer","raw_affiliation_strings":["Department of Mathematics, Lahore College for Women University, Lahore, Pakistan"],"raw_orcid":"https://orcid.org/0000-0003-2792-1670","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Lahore College for Women University, Lahore, Pakistan","institution_ids":["https://openalex.org/I161237661"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080509093","display_name":"Imrana Kousar","orcid":null},"institutions":[{"id":"https://openalex.org/I161237661","display_name":"Lahore College for Women University","ror":"https://ror.org/02bf6br77","country_code":"PK","type":"education","lineage":["https://openalex.org/I161237661"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Imrana Kousar","raw_affiliation_strings":["Department of Mathematics, Lahore College for Women University, Lahore, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Lahore College for Women University, Lahore, Pakistan","institution_ids":["https://openalex.org/I161237661"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101950652","display_name":"Muhammad Awais Umar","orcid":"https://orcid.org/0000-0002-8786-0171"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Muhammad Awais Umar","raw_affiliation_strings":["Government Degree College (B), Sharaqpur Sharif, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-8786-0171","affiliations":[{"raw_affiliation_string":"Government Degree College (B), Sharaqpur Sharif, Pakistan","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078037189","display_name":"Nehad Ali Shah","orcid":"https://orcid.org/0000-0002-1949-5643"},"institutions":[{"id":"https://openalex.org/I141445968","display_name":"Ton Duc Thang University","ror":"https://ror.org/01drq0835","country_code":"VN","type":"education","lineage":["https://openalex.org/I141445968"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"Nehad Ali Shah","raw_affiliation_strings":["Faculty of Mathematics & Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam","Informetrics Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam"],"raw_orcid":"https://orcid.org/0000-0002-1949-5643","affiliations":[{"raw_affiliation_string":"Faculty of Mathematics & Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam","institution_ids":["https://openalex.org/I141445968"]},{"raw_affiliation_string":"Informetrics Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam","institution_ids":["https://openalex.org/I141445968"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5018970039"],"corresponding_institution_ids":["https://openalex.org/I2800350601"],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":0.5826,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.7316601,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"8","issue":null,"first_page":"109801","last_page":"109806"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9998999834060669,"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/T12541","display_name":"Graph Labeling and Dimension Problems","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/T10374","display_name":"Advanced Graph Theory Research","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/T11797","display_name":"graph theory and CDMA systems","score":0.9990000128746033,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5520949363708496},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5360899567604065},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5181421041488647},{"id":"https://openalex.org/keywords/secrecy","display_name":"Secrecy","score":0.4261196255683899},{"id":"https://openalex.org/keywords/wireless","display_name":"Wireless","score":0.41303756833076477},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37499386072158813},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37032437324523926},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3228430151939392},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3068283796310425},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.1363791823387146}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5520949363708496},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5360899567604065},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5181421041488647},{"id":"https://openalex.org/C2776452267","wikidata":"https://www.wikidata.org/wiki/Q1503443","display_name":"Secrecy","level":2,"score":0.4261196255683899},{"id":"https://openalex.org/C555944384","wikidata":"https://www.wikidata.org/wiki/Q249","display_name":"Wireless","level":2,"score":0.41303756833076477},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37499386072158813},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37032437324523926},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3228430151939392},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3068283796310425},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.1363791823387146},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2020.3002397","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.3002397","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/09116989.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:90fd85fffe7848d682cb83b277230389","is_oa":true,"landing_page_url":"https://doaj.org/article/90fd85fffe7848d682cb83b277230389","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,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 8, Pp 109801-109806 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2020.3002397","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.3002397","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/09116989.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3034758533.pdf","grobid_xml":"https://content.openalex.org/works/W3034758533.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W172950155","https://openalex.org/W2001389909","https://openalex.org/W2028341678","https://openalex.org/W2056891496","https://openalex.org/W2056979696","https://openalex.org/W2112641412","https://openalex.org/W2116370293","https://openalex.org/W2123348176","https://openalex.org/W2148410650","https://openalex.org/W2404127378","https://openalex.org/W2614036046","https://openalex.org/W2741560118","https://openalex.org/W2771087721","https://openalex.org/W2809722786","https://openalex.org/W2915992390","https://openalex.org/W2921947540","https://openalex.org/W2948721318","https://openalex.org/W2969378592","https://openalex.org/W2975556440","https://openalex.org/W2975793915","https://openalex.org/W2982098067","https://openalex.org/W2995879012","https://openalex.org/W2995958570","https://openalex.org/W3037105314","https://openalex.org/W4234956562","https://openalex.org/W6607040268","https://openalex.org/W6639106650","https://openalex.org/W6676813938","https://openalex.org/W6713657272","https://openalex.org/W6737619244"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2493929861","https://openalex.org/W2016567611","https://openalex.org/W2475541339","https://openalex.org/W565335793","https://openalex.org/W2363071176","https://openalex.org/W2107199751","https://openalex.org/W4243812570","https://openalex.org/W4300441478","https://openalex.org/W2062965938"],"abstract_inverted_index":{"Many":[0],"variations":[1],"of":[2,28,35,37,44,74,87,129,144,157,169],"graph":[3,45,76,124,146],"labeling":[4,16,60,73,132,156],"has":[5],"been":[6],"defined":[7],"in":[8,22,123],"the":[9,38,42,49,85,135,149],"literature.":[10],"e.g.,":[11],"graceful,":[12],"harmonious":[13],"and":[14,21,33,108,117,121,141],"radio":[15,59,71,131,142,155,167],"etc.":[17],"In":[18,52,159],"information":[19],"technology":[20],"data":[23],"sciences,":[24],"we":[25,55,162],"need":[26],"secrecy":[27],"data,":[29],"different":[30],"channel":[31,63],"assignment":[32,64],"accuracy":[34],"transmission":[36],"data.":[39],"This":[40],"make":[41],"use":[43],"terminologies":[46],"indispensable":[47],"for":[48,62,166],"computer":[50],"programs.":[51],"this":[53,160],"paper,":[54],"will":[56,163],"discuss":[57],"multi-distance":[58],"used":[61],"problem":[65],"over":[66,153],"a":[67,75,79,130,145,170],"wireless":[68],"communication.":[69],"A":[70],"(multi-distance)":[72],"G":[77,125,147],"is":[78,134,148],"function":[80],"h":[81,133,140],"from":[82],"V(G)":[83],"to":[84],"set":[86],"non-negative":[88],"integers":[89],"such":[90],"that":[91],"|h(u)":[92],"-":[93,99],"h(v)|":[94],"\u2265":[95,184],"diam(G)":[96,107],"+":[97],"1":[98],"d":[100,109],"<sub":[101,110,174,179],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[102,111,175,180],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">G</sub>":[103,112],"(u,":[104,113],"v),":[105],"Where":[106],"v)":[114],"are":[115],"diameter":[116],"distance":[118],"between":[119],"u":[120],"v":[122],"respectively.":[126],"The":[127],"span":[128,151],"maximum":[136],"integer":[137],"assigned":[138],"by":[139],"number":[143,168],"minimum":[150],"taken":[152],"all":[154],"G.":[158],"article,":[161],"find":[164],"relations":[165],"strong":[171],"product":[172],"K":[173],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">3</sub>":[176],"\u2297":[177],"P":[178],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</sub>":[181],",":[182],"n":[183],"3.":[185]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}