{"id":"https://openalex.org/W4385349867","doi":"https://doi.org/10.61091/ars156-02","title":"Further Results on Radio Number of Wedge sum of Graphs","display_name":"Further Results on Radio Number of Wedge sum of Graphs","publication_year":2023,"publication_date":"2023-07-28","ids":{"openalex":"https://openalex.org/W4385349867","doi":"https://doi.org/10.61091/ars156-02"},"language":"en","primary_location":{"id":"doi:10.61091/ars156-02","is_oa":true,"landing_page_url":"http://dx.doi.org/10.61091/ars156-02","pdf_url":"https://combinatorialpress.com/article/ars/Further-Results-on-Radio-Number-ofWedge-sum-of-Graphs.pdf","source":{"id":"https://openalex.org/S73158690","display_name":"Ars Combinatoria","issn_l":"0381-7032","issn":["0381-7032","2817-5204"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4323439501","host_organization_name":"Charles Babbage Research Centre","host_organization_lineage":["https://openalex.org/P4323439501"],"host_organization_lineage_names":["Charles Babbage Research Centre"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Ars Combinatoria","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://combinatorialpress.com/article/ars/Further-Results-on-Radio-Number-ofWedge-sum-of-Graphs.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023886397","display_name":"Asim Naseem","orcid":"https://orcid.org/0000-0002-7032-3310"},"institutions":[{"id":"https://openalex.org/I43879129","display_name":"Government College University, Lahore","ror":"https://ror.org/040gec961","country_code":"PK","type":"education","lineage":["https://openalex.org/I43879129"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Asim Naseem","raw_affiliation_strings":["Department of Mathematics, Government College University, Lahore, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Government College University, Lahore, Pakistan","institution_ids":["https://openalex.org/I43879129"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032351563","display_name":"Khurram Shabbir","orcid":"https://orcid.org/0000-0001-6613-6339"},"institutions":[{"id":"https://openalex.org/I43879129","display_name":"Government College University, Lahore","ror":"https://ror.org/040gec961","country_code":"PK","type":"education","lineage":["https://openalex.org/I43879129"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Khurram Shabbir","raw_affiliation_strings":["Department of Mathematics, Government College University, Lahore, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Government College University, Lahore, Pakistan","institution_ids":["https://openalex.org/I43879129"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044532307","display_name":"Muhammad Ramzan","orcid":"https://orcid.org/0000-0002-2885-3617"},"institutions":[{"id":"https://openalex.org/I43879129","display_name":"Government College University, Lahore","ror":"https://ror.org/040gec961","country_code":"PK","type":"education","lineage":["https://openalex.org/I43879129"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"M. Ramzan","raw_affiliation_strings":["Department of Mathematics, Government College University, Lahore, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Government College University, Lahore, Pakistan","institution_ids":["https://openalex.org/I43879129"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5023886397"],"corresponding_institution_ids":["https://openalex.org/I43879129"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.15335133,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"156","issue":null,"first_page":"13","last_page":"23"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9951000213623047,"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":0.9948999881744385,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.80838942527771},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6147120594978333},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5339540243148804},{"id":"https://openalex.org/keywords/injective-function","display_name":"Injective function","score":0.48024919629096985},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4513401985168457},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3881543278694153}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.80838942527771},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6147120594978333},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5339540243148804},{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.48024919629096985},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4513401985168457},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3881543278694153}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.61091/ars156-02","is_oa":true,"landing_page_url":"http://dx.doi.org/10.61091/ars156-02","pdf_url":"https://combinatorialpress.com/article/ars/Further-Results-on-Radio-Number-ofWedge-sum-of-Graphs.pdf","source":{"id":"https://openalex.org/S73158690","display_name":"Ars Combinatoria","issn_l":"0381-7032","issn":["0381-7032","2817-5204"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4323439501","host_organization_name":"Charles Babbage Research Centre","host_organization_lineage":["https://openalex.org/P4323439501"],"host_organization_lineage_names":["Charles Babbage Research Centre"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Ars Combinatoria","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.61091/ars156-02","is_oa":true,"landing_page_url":"http://dx.doi.org/10.61091/ars156-02","pdf_url":"https://combinatorialpress.com/article/ars/Further-Results-on-Radio-Number-ofWedge-sum-of-Graphs.pdf","source":{"id":"https://openalex.org/S73158690","display_name":"Ars Combinatoria","issn_l":"0381-7032","issn":["0381-7032","2817-5204"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4323439501","host_organization_name":"Charles Babbage Research Centre","host_organization_lineage":["https://openalex.org/P4323439501"],"host_organization_lineage_names":["Charles Babbage Research Centre"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Ars Combinatoria","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4385349867.pdf","grobid_xml":"https://content.openalex.org/works/W4385349867.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W389634923","https://openalex.org/W2056979696","https://openalex.org/W2112641412","https://openalex.org/W2614036046","https://openalex.org/W2771087721","https://openalex.org/W2775422231","https://openalex.org/W2918864036"],"related_works":["https://openalex.org/W2092595544","https://openalex.org/W2782453491","https://openalex.org/W4287867392","https://openalex.org/W4302772626","https://openalex.org/W3006382266","https://openalex.org/W1524617299","https://openalex.org/W782241198","https://openalex.org/W1719252778","https://openalex.org/W922283457","https://openalex.org/W2066729569"],"abstract_inverted_index":{"Let":[0,164,209],"G":[1,37,106,117,125,147],"be":[2,179,232],"a":[3,33,120],"simple":[4],"connected":[5],"graph":[6],"with":[7],"vertex":[8,122,185],"set":[9],"V":[10,20,67],"and":[11,82,257,300],"diameter":[12],"d":[13,50,57,70],".":[14,84,101,118,163,208,273,323],"An":[15],"injective":[16],"function":[17],"c":[18,40,44,92,100],":":[19],"\u2192":[21],"{":[22],"1":[23,59,131,169,198,213,216,247,261,290,304,307],",":[24,26,28,53,64,68,73,126,132,135,137,148,170,173,175,199,202,204,217,223,225,248,251,253,262,266,268,291,294,296,308,314,316],"2":[25,134,172,190,201,219,222,250,265,293,310,313],"3":[27],"\u2026":[29,136,174,203,224,252,267,295,315],"}":[30],"is":[31,76,93,107,141,152,161],"called":[32,94,142],"radio":[34,103,114,280],"labeling":[35,99],"of":[36,91,97,105,116,124,146,155,187,236,239,285],"if":[38],"|":[39,48],"(":[41,45,51,71,129,167,196,211,245,258,288,302],"x":[42,52,63,72,81],")":[43,47,55,75,140,178,207,231,256,272,299,322],"y":[46,54,65,74,83],"+":[49,58],"\u2265":[56,189],"for":[60,282],"all":[61,113],"distinct":[62],"\u2208":[66],"where":[69,149],"the":[77,89,95,98,108,127,143,153,180,233,279],"distance":[78,158],"between":[79],"vertices":[80,156],"The":[85,102],"largest":[86],"number":[87,104,154,281],"in":[88],"range":[90],"span":[96,110],"minimum":[109],"taken":[111],"over":[112],"labelings":[115],"For":[119],"fixed":[121],"z":[123,160],"sequence":[128],"l":[130,133,138,150,168,171,176,197,200,205,212,214,218,220,226,228,246,249,254,259,263,269,289,292,297,303,305,309,311,317,319],"r":[139,177,206,227,230,255,271,298,318,321],"level":[144,194,243],"tuple":[145,195],"i":[151,162],"whose":[157],"from":[159],"J":[165,210,286,301],"k":[166,188,287],"wedge":[181,234],"sum":[182,235],"(i.e.":[183],"one":[184],"union)":[186],"graphs":[191,238],"having":[192,242],"same":[193,240],"\u2032":[215,221,229,260,264,270,306,312,320],"two":[237],"order,":[241],"tuples":[244],"In":[274],"this":[275],"paper,":[276],"we":[277],"compute":[278],"some":[283],"sub-families":[284]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2023-07-29T00:00:00"}