{"id":"https://openalex.org/W2118403623","doi":"https://doi.org/10.1142/s1793830914500682","title":"A generalization of commuting graphs","display_name":"A generalization of commuting graphs","publication_year":2014,"publication_date":"2014-09-18","ids":{"openalex":"https://openalex.org/W2118403623","doi":"https://doi.org/10.1142/s1793830914500682","mag":"2118403623"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830914500682","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830914500682","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019177905","display_name":"Mojgan Afkhami","orcid":"https://orcid.org/0000-0002-6819-3086"},"institutions":[{"id":"https://openalex.org/I1312987727","display_name":"University of Neyshabur","ror":"https://ror.org/01x41eb05","country_code":"IR","type":"education","lineage":["https://openalex.org/I1312987727"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"M. Afkhami","raw_affiliation_strings":["Department of Mathematics, University of Neyshabur, P. O. Box 91136-899, Neyshabur, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Neyshabur, P. O. Box 91136-899, Neyshabur, Iran","institution_ids":["https://openalex.org/I1312987727"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003834542","display_name":"Zahra Barati","orcid":"https://orcid.org/0000-0003-0107-4805"},"institutions":[{"id":"https://openalex.org/I2800768525","display_name":"University of Bojnord","ror":"https://ror.org/05khxfe53","country_code":"IR","type":"education","lineage":["https://openalex.org/I2800768525"]},{"id":"https://openalex.org/I4210107575","display_name":"Kosar University of Bojnord","ror":"https://ror.org/01e7e7r31","country_code":"IR","type":"education","lineage":["https://openalex.org/I4210107575"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Z. Barati","raw_affiliation_strings":["Department of Mathematics, Kosar University of Bojnord, P. O. Box 9415615458, Bojnord, Iran","Department of Mathematics, Kosar University of Bojnord, P. O. Box 9415615458, Bojnord, Iran#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Kosar University of Bojnord, P. O. Box 9415615458, Bojnord, Iran","institution_ids":["https://openalex.org/I2800768525","https://openalex.org/I4210107575"]},{"raw_affiliation_string":"Department of Mathematics, Kosar University of Bojnord, P. O. Box 9415615458, Bojnord, Iran#TAB#","institution_ids":["https://openalex.org/I2800768525","https://openalex.org/I4210107575"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084145606","display_name":"Nesa Hoseini","orcid":null},"institutions":[{"id":"https://openalex.org/I86958956","display_name":"Ferdowsi University of Mashhad","ror":"https://ror.org/00g6ka752","country_code":"IR","type":"education","lineage":["https://openalex.org/I86958956"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"N. Hoseini","raw_affiliation_strings":["Department of Pure Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159-91775, Mashhad, Iran","Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159-#N#91775, Mashhad, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159-91775, Mashhad, Iran","institution_ids":["https://openalex.org/I86958956"]},{"raw_affiliation_string":"Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159-#N#91775, Mashhad, Iran","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067556620","display_name":"Kazem Khashyarmanesh","orcid":"https://orcid.org/0000-0003-3314-7298"},"institutions":[{"id":"https://openalex.org/I86958956","display_name":"Ferdowsi University of Mashhad","ror":"https://ror.org/00g6ka752","country_code":"IR","type":"education","lineage":["https://openalex.org/I86958956"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"K. Khashyarmanesh","raw_affiliation_strings":["Department of Pure Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159-91775, Mashhad, Iran","Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159-#N#91775, Mashhad, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159-91775, Mashhad, Iran","institution_ids":["https://openalex.org/I86958956"]},{"raw_affiliation_string":"Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159-#N#91775, Mashhad, Iran","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5019177905"],"corresponding_institution_ids":["https://openalex.org/I1312987727"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.18556281,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"07","issue":"01","first_page":"1450068","last_page":"1450068"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9994000196456909,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9994000196456909,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.9984999895095825,"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/T10849","display_name":"Finite Group Theory Research","score":0.9898999929428101,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/combinatorics","display_name":"Combinatorics","score":0.7555480599403381},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6510087251663208},{"id":"https://openalex.org/keywords/planarity-testing","display_name":"Planarity testing","score":0.5800477266311646},{"id":"https://openalex.org/keywords/endomorphism","display_name":"Endomorphism","score":0.5561879277229309},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.508796751499176},{"id":"https://openalex.org/keywords/symmetric-graph","display_name":"Symmetric graph","score":0.5045047998428345},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4776698052883148},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4752216935157776},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4426546096801758},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.4180780053138733},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.32763993740081787},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.26463183760643005}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7555480599403381},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6510087251663208},{"id":"https://openalex.org/C68260962","wikidata":"https://www.wikidata.org/wiki/Q7200967","display_name":"Planarity testing","level":2,"score":0.5800477266311646},{"id":"https://openalex.org/C116858840","wikidata":"https://www.wikidata.org/wiki/Q1340800","display_name":"Endomorphism","level":2,"score":0.5561879277229309},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.508796751499176},{"id":"https://openalex.org/C14201764","wikidata":"https://www.wikidata.org/wiki/Q1205074","display_name":"Symmetric graph","level":5,"score":0.5045047998428345},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4776698052883148},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4752216935157776},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4426546096801758},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.4180780053138733},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.32763993740081787},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.26463183760643005},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830914500682","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830914500682","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1484040084","https://openalex.org/W1989280699","https://openalex.org/W1990034619","https://openalex.org/W2022878275","https://openalex.org/W2028134290","https://openalex.org/W2041603746","https://openalex.org/W2072083712","https://openalex.org/W2108587835"],"related_works":["https://openalex.org/W2373079339","https://openalex.org/W2108284102","https://openalex.org/W3047848516","https://openalex.org/W4287691299","https://openalex.org/W4297837089","https://openalex.org/W183093845","https://openalex.org/W2951726931","https://openalex.org/W4293351855","https://openalex.org/W4384811834","https://openalex.org/W2964235359"],"abstract_inverted_index":{"Let":[0],"R":[1,15,38,48,81,95],"be":[2,11,18],"a":[3,19,27,30,42],"ring":[4],"with":[5,45],"the":[6,87,92],"identity":[7],"element":[8],"1,":[9],"\u03b1":[10],"an":[12,59],"endomorphism":[13],"of":[14,29,79,91],"and":[16,55,66,89],"\u03b4":[17],"left":[20],"\u03b1-derivation.":[21],"In":[22],"this":[23],"paper,":[24],"we":[25,85],"introduce":[26],"generalization":[28],"commuting":[31],"graph,":[32],"which":[33],"is":[34,58],"denoted":[35],"by":[36],"\u0393":[37,80,94],"(\u03b1,":[39,82,96],"\u03b4),":[40],"as":[41],"directed":[43],"graph":[44,93],"vertex":[46],"set":[47],"and,":[49],"for":[50],"two":[51],"distinct":[52],"vertices":[53],"x":[54,62],"y,":[56],"there":[57],"arc":[60],"from":[61],"to":[63],"y":[64],"if":[65,68],"only":[67],"xy":[69],"=":[70],"\u03b1(y)x":[71],"+":[72],"\u03b4(y).":[73],"We":[74],"study":[75],"some":[76],"basic":[77],"properties":[78],"\u03b4).":[83],"Also,":[84],"investigate":[86],"planarity":[88],"genus":[90],"0).":[97]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}