{"id":"https://openalex.org/W1525019364","doi":"https://doi.org/10.37236/3654","title":"Zero-Sum Magic Labelings and Null Sets of Regular Graphs","display_name":"Zero-Sum Magic Labelings and Null Sets of Regular Graphs","publication_year":2014,"publication_date":"2014-05-02","ids":{"openalex":"https://openalex.org/W1525019364","doi":"https://doi.org/10.37236/3654","mag":"1525019364"},"language":"en","primary_location":{"id":"doi:10.37236/3654","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3654","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v21i2p17/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v21i2p17/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060541368","display_name":"Saieed Akbari","orcid":"https://orcid.org/0000-0001-8994-8858"},"institutions":[{"id":"https://openalex.org/I133529467","display_name":"Sharif University of Technology","ror":"https://ror.org/024c2fq17","country_code":"IR","type":"education","lineage":["https://openalex.org/I133529467"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Saieed Akbari","raw_affiliation_strings":["Sharif University of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sharif University of Technology","institution_ids":["https://openalex.org/I133529467"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055832370","display_name":"Farhad Rahmati","orcid":"https://orcid.org/0000-0002-4859-6179"},"institutions":[{"id":"https://openalex.org/I158248296","display_name":"Amirkabir University of Technology","ror":"https://ror.org/04gzbav43","country_code":"IR","type":"education","lineage":["https://openalex.org/I158248296"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Farhad Rahmati","raw_affiliation_strings":["Amirkabir University of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Amirkabir University of Technology","institution_ids":["https://openalex.org/I158248296"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064233496","display_name":"S. Zare","orcid":null},"institutions":[{"id":"https://openalex.org/I158248296","display_name":"Amirkabir University of Technology","ror":"https://ror.org/04gzbav43","country_code":"IR","type":"education","lineage":["https://openalex.org/I158248296"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Sanaz Zare","raw_affiliation_strings":["Amirkabir University of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Amirkabir University of Technology","institution_ids":["https://openalex.org/I158248296"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8357,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.84366416,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"21","issue":"2","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":1.0,"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":1.0,"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":0.9377999901771545,"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/combinatorics","display_name":"Combinatorics","score":0.8969700336456299},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7316321134567261},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6926669478416443},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.6910825967788696},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5601001381874084},{"id":"https://openalex.org/keywords/magic","display_name":"MAGIC (telescope)","score":0.5215916037559509},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.4260762631893158},{"id":"https://openalex.org/keywords/complete-bipartite-graph","display_name":"Complete bipartite graph","score":0.41290903091430664},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3595764935016632},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14629092812538147}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8969700336456299},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7316321134567261},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6926669478416443},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.6910825967788696},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5601001381874084},{"id":"https://openalex.org/C2777704519","wikidata":"https://www.wikidata.org/wiki/Q45732","display_name":"MAGIC (telescope)","level":2,"score":0.5215916037559509},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.4260762631893158},{"id":"https://openalex.org/C134119311","wikidata":"https://www.wikidata.org/wiki/Q913598","display_name":"Complete bipartite graph","level":4,"score":0.41290903091430664},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3595764935016632},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14629092812538147},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/3654","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3654","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v21i2p17/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/3654","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3654","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v21i2p17/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320323627","display_name":"School of Mathematics, Institute for Research in Fundamental Sciences","ror":"https://ror.org/04xreqs31"},{"id":"https://openalex.org/F4320323645","display_name":"Institute for Research in Fundamental Sciences","ror":"https://ror.org/04xreqs31"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1525019364.pdf","grobid_xml":"https://content.openalex.org/works/W1525019364.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W606453859","https://openalex.org/W1537052798","https://openalex.org/W1604413132","https://openalex.org/W1883770995","https://openalex.org/W2078014870","https://openalex.org/W2088648195","https://openalex.org/W2105006345","https://openalex.org/W2105800562","https://openalex.org/W2122550743","https://openalex.org/W2335389215","https://openalex.org/W2343484179","https://openalex.org/W2403360495","https://openalex.org/W2412721794","https://openalex.org/W2477320853","https://openalex.org/W2552725029","https://openalex.org/W2725535249","https://openalex.org/W6609102973","https://openalex.org/W6681462111","https://openalex.org/W6817237904","https://openalex.org/W6819024496"],"related_works":["https://openalex.org/W2405987656","https://openalex.org/W2369757561","https://openalex.org/W2054383364","https://openalex.org/W1491930737","https://openalex.org/W2587433615","https://openalex.org/W1779359754","https://openalex.org/W2089088747","https://openalex.org/W3210704652","https://openalex.org/W2018678447","https://openalex.org/W1988771411"],"abstract_inverted_index":{"For":[0],"every":[1],"$h\\in":[2],"\\mathbb{N}$,":[3],"a":[4,25,53,66,74,96,150,169],"graph":[5,75,154],"$G$":[6,64,94,117,148,167],"with":[7],"the":[8,13,35,81,102],"vertex":[9,37],"set":[10,15,72,82],"$V(G)$":[11],"and":[12,130,147],"edge":[14],"$E(G)$":[16],"is":[17,52,59,80,118,145,149,168],"said":[18],"to":[19],"be":[20],"$h$-magic":[21,68,98],"if":[22,116,143,166],"there":[23],"exists":[24],"labeling":[26,38],"$l":[27],":":[28,40],"E(G)":[29],"\\rightarrow\\mathbb{Z}_h":[30],"\\setminus":[31,136,160,176],"\\{0\\}$":[32],"such":[33,92],"that":[34,63,93,115,142,165],"induced":[36],"$s":[39],"V":[41],"(G)":[42],"\\rightarrow":[43],"\\mathbb{Z}_h$,":[44],"defined":[45],"by":[46,78],"$s(v)":[47],"=\\sum_{uv":[48],"\\in":[49,88],"E(G)}":[50],"l(uv)$":[51],"constant":[54,58],"map.":[55],"When":[56],"this":[57,111],"zero,":[60],"we":[61,113,140,163],"say":[62],"admits":[65,95],"zero-sum":[67,97],"labeling.":[69,99],"The":[70],"null":[71,103],"of":[73,83,105],"$G$,":[76],"denoted":[77],"$N(G)$,":[79],"all":[84],"natural":[85],"numbers":[86],"$h":[87],"\\mathbb{":[89],"N}":[90],"$":[91,158],"In":[100,110],"2012,":[101],"sets":[104],"3-regular":[106],"graphs":[107],"were":[108],"determined.":[109],"paper":[112],"show":[114,164],"an":[119],"$r$-regular":[120,153],"graph,":[121,173],"then":[122,157,174],"for":[123,131],"even":[124],"$r$":[125,133,144],"($r":[126],"&gt;":[127],"2$),":[128],"$N(G)=\\mathbb{N}$":[129],"odd":[132,146],"($r\\neq5$),":[134],"$\\mathbb{N}":[135,175],"\\{2,4\\}\\subseteq":[137],"N(G)$.":[138,178],"Moreover,":[139],"prove":[141],"$2$-edge":[151,170],"connected":[152,171],"($r\\neq":[155],"5$),":[156],"N(G)=\\mathbb{N}":[159],"\\{2\\}$.":[161],"Also,":[162],"bipartite":[172],"\\{2,3,4,5\\}\\subseteq":[177]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
