{"id":"https://openalex.org/W4415764939","doi":"https://doi.org/10.5614/ejgta.2025.13.2.5","title":"On the sigma chromatic number of the ideal-based zero divisor graphs of the ring of integers modulo n","display_name":"On the sigma chromatic number of the ideal-based zero divisor graphs of the ring of integers modulo n","publication_year":2025,"publication_date":"2025-10-28","ids":{"openalex":"https://openalex.org/W4415764939","doi":"https://doi.org/10.5614/ejgta.2025.13.2.5"},"language":"en","primary_location":{"id":"doi:10.5614/ejgta.2025.13.2.5","is_oa":true,"landing_page_url":"https://doi.org/10.5614/ejgta.2025.13.2.5","pdf_url":"http://ejgta.org/index.php/ejgta/article/download/1652/pdf_333","source":{"id":"https://openalex.org/S4210230765","display_name":"Electronic Journal of Graph Theory and Applications","issn_l":"2338-2287","issn":["2338-2287"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315132","host_organization_name":"Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Austr","host_organization_lineage":["https://openalex.org/P4310315132"],"host_organization_lineage_names":["Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Austr"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Journal of Graph Theory and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"http://ejgta.org/index.php/ejgta/article/download/1652/pdf_333","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Agnes D. Garciano","orcid":null},"institutions":[{"id":"https://openalex.org/I19722","display_name":"Ateneo de Manila University","ror":"https://ror.org/053kevk63","country_code":"PH","type":"education","lineage":["https://openalex.org/I19722"]}],"countries":["PH"],"is_corresponding":false,"raw_author_name":"Agnes D. Garciano","raw_affiliation_strings":["Ateneo de Manila University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ateneo de Manila University","institution_ids":["https://openalex.org/I19722"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Reginaldo M. Marcelo","orcid":null},"institutions":[{"id":"https://openalex.org/I19722","display_name":"Ateneo de Manila University","ror":"https://ror.org/053kevk63","country_code":"PH","type":"education","lineage":["https://openalex.org/I19722"]}],"countries":["PH"],"is_corresponding":false,"raw_author_name":"Reginaldo M. Marcelo","raw_affiliation_strings":["Ateneo de Manila University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ateneo de Manila University","institution_ids":["https://openalex.org/I19722"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020253829","display_name":"Mari-Jo P. Ruiz","orcid":null},"institutions":[{"id":"https://openalex.org/I19722","display_name":"Ateneo de Manila University","ror":"https://ror.org/053kevk63","country_code":"PH","type":"education","lineage":["https://openalex.org/I19722"]}],"countries":["PH"],"is_corresponding":false,"raw_author_name":"Mari-Jo P. Ruiz","raw_affiliation_strings":["Ateneo de Manila University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ateneo de Manila University","institution_ids":["https://openalex.org/I19722"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021314399","display_name":"Mark Anthony C. Tolentino","orcid":"https://orcid.org/0000-0001-8863-3002"},"institutions":[{"id":"https://openalex.org/I19722","display_name":"Ateneo de Manila University","ror":"https://ror.org/053kevk63","country_code":"PH","type":"education","lineage":["https://openalex.org/I19722"]}],"countries":["PH"],"is_corresponding":false,"raw_author_name":"Mark Anthony Cayanan Tolentino","raw_affiliation_strings":["Ateneo de Manila University"],"raw_orcid":"https://orcid.org/0000-0001-8863-3002","affiliations":[{"raw_affiliation_string":"Ateneo de Manila University","institution_ids":["https://openalex.org/I19722"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I19722"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.3751634,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":"2","first_page":"295","last_page":"295"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9753999710083008,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.9753999710083008,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.008500000461935997,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.0034000000450760126,"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/vertex","display_name":"Vertex (graph theory)","score":0.5480999946594238},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.4867999851703644},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.48669999837875366},{"id":"https://openalex.org/keywords/sigma","display_name":"Sigma","score":0.46149998903274536},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.45980000495910645},{"id":"https://openalex.org/keywords/brooks-theorem","display_name":"Brooks' theorem","score":0.4368000030517578},{"id":"https://openalex.org/keywords/zero-divisor","display_name":"Zero divisor","score":0.41609999537467957},{"id":"https://openalex.org/keywords/commutative-ring","display_name":"Commutative ring","score":0.4074000120162964}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8636999726295471},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.786899983882904},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5480999946594238},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5029000043869019},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.4867999851703644},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.48669999837875366},{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.46149998903274536},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.45980000495910645},{"id":"https://openalex.org/C51658606","wikidata":"https://www.wikidata.org/wiki/Q512897","display_name":"Brooks' theorem","level":5,"score":0.4368000030517578},{"id":"https://openalex.org/C9555016","wikidata":"https://www.wikidata.org/wiki/Q828111","display_name":"Zero divisor","level":2,"score":0.41609999537467957},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.4074000120162964},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.3686999976634979},{"id":"https://openalex.org/C76946457","wikidata":"https://www.wikidata.org/wiki/Q504843","display_name":"Graph coloring","level":3,"score":0.34439998865127563},{"id":"https://openalex.org/C158319403","wikidata":"https://www.wikidata.org/wiki/Q5477527","display_name":"Fractional coloring","level":5,"score":0.3440000116825104},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.3102000057697296},{"id":"https://openalex.org/C123809776","wikidata":"https://www.wikidata.org/wiki/Q1050972","display_name":"Edge coloring","level":5,"score":0.2957000136375427},{"id":"https://openalex.org/C28093856","wikidata":"https://www.wikidata.org/wiki/Q835614","display_name":"Petersen graph","level":5,"score":0.29330000281333923},{"id":"https://openalex.org/C70488441","wikidata":"https://www.wikidata.org/wiki/Q5504427","display_name":"Friendship graph","level":5,"score":0.2858000099658966},{"id":"https://openalex.org/C148364342","wikidata":"https://www.wikidata.org/wiki/Q948887","display_name":"Wheel graph","level":5,"score":0.28529998660087585},{"id":"https://openalex.org/C73380178","wikidata":"https://www.wikidata.org/wiki/Q8024306","display_name":"Windmill graph","level":5,"score":0.28029999136924744},{"id":"https://openalex.org/C21642379","wikidata":"https://www.wikidata.org/wiki/Q3342988","display_name":"Complete coloring","level":5,"score":0.272599995136261},{"id":"https://openalex.org/C121134508","wikidata":"https://www.wikidata.org/wiki/Q4949882","display_name":"Bound graph","level":5,"score":0.25519999861717224},{"id":"https://openalex.org/C125080357","wikidata":"https://www.wikidata.org/wiki/Q45715","display_name":"Complete graph","level":3,"score":0.2524000108242035}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5614/ejgta.2025.13.2.5","is_oa":true,"landing_page_url":"https://doi.org/10.5614/ejgta.2025.13.2.5","pdf_url":"http://ejgta.org/index.php/ejgta/article/download/1652/pdf_333","source":{"id":"https://openalex.org/S4210230765","display_name":"Electronic Journal of Graph Theory and Applications","issn_l":"2338-2287","issn":["2338-2287"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315132","host_organization_name":"Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Austr","host_organization_lineage":["https://openalex.org/P4310315132"],"host_organization_lineage_names":["Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Austr"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Journal of Graph Theory and Applications","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:e6a584e1103a4bb49bc614fe98da84cc","is_oa":true,"landing_page_url":"https://doaj.org/article/e6a584e1103a4bb49bc614fe98da84cc","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":"Electronic Journal of Graph Theory and Applications, Vol 13, Iss 2, Pp 295-307 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.5614/ejgta.2025.13.2.5","is_oa":true,"landing_page_url":"https://doi.org/10.5614/ejgta.2025.13.2.5","pdf_url":"http://ejgta.org/index.php/ejgta/article/download/1652/pdf_333","source":{"id":"https://openalex.org/S4210230765","display_name":"Electronic Journal of Graph Theory and Applications","issn_l":"2338-2287","issn":["2338-2287"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315132","host_organization_name":"Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Austr","host_organization_lineage":["https://openalex.org/P4310315132"],"host_organization_lineage_names":["Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Austr"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Journal of Graph Theory and Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320323581","display_name":"Ateneo de Manila University","ror":"https://ror.org/053kevk63"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415764939.pdf","grobid_xml":"https://content.openalex.org/works/W4415764939.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0,131],"objective":[1],"of":[2,34,118,126,135,148,155,168,172,174],"this":[3,159],"paper":[4],"is":[5,42,96,137,142],"to":[6,17],"investigate":[7],"a":[8,22,30,85,89,97,127,152],"particular":[9],"graph":[10,38,47,86],"coloring,":[11,14],"called":[12],"sigma":[13,90,132,153,165],"as":[15,44,144],"applied":[16],"ideal-based":[18,169],"zero-divisor":[19,170],"graphs.":[20],"Given":[21],"commutative":[23],"ring":[24],"R":[25,35,54,65],"with":[26,48],"(nonzero)":[27],"identity":[28],"and":[29,69,141],"proper":[31],"ideal":[32],"I":[33,40,56,60,67,77],",":[36,88,112],"the":[37,81,116,145,164],"\u0393":[39],"(R)":[41],"defined":[43,143],"an":[45],"undirected":[46],"vertex":[49,128],"set":[50,71],"{":[51,72],"x":[52,129],"\u2208":[53,59,64,76],"\\":[55,66],":":[57,74],"xy":[58,73,75],"for":[61,104,151],"some":[62],"y":[63,125],"}":[68,78],"edge":[70],".":[79,130,157,178],"On":[80],"other":[82],"hand,":[83],"given":[84],"G":[87,111,136,156],"coloring":[91,98,154],"c:":[92],"V(G)":[93],"\u2192":[94],"\u2115":[95],"that":[99],"satisfies":[100],"\u03c3(u)":[101],"\u2260":[102],"\u03c3(v)":[103],"any":[105],"two":[106],"adjacent":[107],"vertices":[108],"u,v":[109],"in":[110],"where":[113],"\u03c3(x)":[114],"denotes":[115],"sum":[117],"all":[119,123],"colors":[120,149],"c(y)":[121],"among":[122],"neighbors":[124],"chromatic":[133,166],"number":[134,147,167],"denoted":[138],"by":[139],"\u03c3(G)":[140],"fewest":[146],"needed":[150],"In":[158],"paper,":[160],"we":[161],"completely":[162],"determine":[163],"graphs":[171],"rings":[173],"integers":[175],"modulo":[176],"n":[177]},"counts_by_year":[],"updated_date":"2026-08-23T07:36:19.812096","created_date":"2025-11-01T00:00:00"}
