{"id":"https://openalex.org/W2735538877","doi":"https://doi.org/10.1142/s1793830917500550","title":"Counting and enumerating unlabeled split\u2013indifference graphs","display_name":"Counting and enumerating unlabeled split\u2013indifference graphs","publication_year":2017,"publication_date":"2017-07-10","ids":{"openalex":"https://openalex.org/W2735538877","doi":"https://doi.org/10.1142/s1793830917500550","mag":"2735538877"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830917500550","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830917500550","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/A5075943018","display_name":"Lilian Markenzon","orcid":"https://orcid.org/0000-0001-7524-6812"},"institutions":[{"id":"https://openalex.org/I122140584","display_name":"Universidade Federal do Rio de Janeiro","ror":"https://ror.org/03490as77","country_code":"BR","type":"education","lineage":["https://openalex.org/I122140584"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Lilian Markenzon","raw_affiliation_strings":["NCE \u2013 Universidade Federal do Rio de Janeiro, Av. Athos da Silveira, 274, Predio do CCMN, Cidade Universitaria, 21941-611, Rio de Janeiro, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"NCE \u2013 Universidade Federal do Rio de Janeiro, Av. Athos da Silveira, 274, Predio do CCMN, Cidade Universitaria, 21941-611, Rio de Janeiro, Brazil","institution_ids":["https://openalex.org/I122140584"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081297199","display_name":"Christina F. E. M. Waga","orcid":"https://orcid.org/0000-0002-3431-7730"},"institutions":[{"id":"https://openalex.org/I40034438","display_name":"Universidade do Estado do Rio de Janeiro","ror":"https://ror.org/0198v2949","country_code":"BR","type":"education","lineage":["https://openalex.org/I40034438"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Christina F. E. M. Waga","raw_affiliation_strings":["IME \u2013 Universidade do Estado do Rio de Janeiro, Rua S\u00e3o Francisco Xavier 524, 20559-900, Rio de Janeiro, Brazil"],"raw_orcid":"https://orcid.org/0000-0002-3431-7730","affiliations":[{"raw_affiliation_string":"IME \u2013 Universidade do Estado do Rio de Janeiro, Rua S\u00e3o Francisco Xavier 524, 20559-900, Rio de Janeiro, Brazil","institution_ids":["https://openalex.org/I40034438"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5075943018"],"corresponding_institution_ids":["https://openalex.org/I122140584"],"apc_list":null,"apc_paid":null,"fwci":0.474,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.66593827,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"09","issue":"04","first_page":"1750055","last_page":"1750055"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998000264167786,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9998000264167786,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9940000176429749,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9830999970436096,"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/mathematics","display_name":"Mathematics","score":0.7897409200668335},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6923736929893494},{"id":"https://openalex.org/keywords/graph-isomorphism","display_name":"Graph isomorphism","score":0.6582716107368469},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.6380132436752319},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.601489782333374},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5434889793395996},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47099488973617554},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4576517641544342},{"id":"https://openalex.org/keywords/induced-subgraph-isomorphism-problem","display_name":"Induced subgraph isomorphism problem","score":0.45515531301498413},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.41494956612586975},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.250424861907959},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14054369926452637},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09392765164375305}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7897409200668335},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6923736929893494},{"id":"https://openalex.org/C61665672","wikidata":"https://www.wikidata.org/wiki/Q303100","display_name":"Graph isomorphism","level":4,"score":0.6582716107368469},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.6380132436752319},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.601489782333374},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5434889793395996},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47099488973617554},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4576517641544342},{"id":"https://openalex.org/C191241153","wikidata":"https://www.wikidata.org/wiki/Q6027240","display_name":"Induced subgraph isomorphism problem","level":5,"score":0.45515531301498413},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.41494956612586975},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.250424861907959},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14054369926452637},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09392765164375305},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","level":1,"score":0.0},{"id":"https://openalex.org/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.0},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.0},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830917500550","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830917500550","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":[{"id":"https://metadata.un.org/sdg/10","score":0.7200000286102295,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W658849301","https://openalex.org/W1984528974","https://openalex.org/W1993232133","https://openalex.org/W1993343925","https://openalex.org/W2002368069","https://openalex.org/W2021806684","https://openalex.org/W2065919728","https://openalex.org/W2072648397","https://openalex.org/W2094338284","https://openalex.org/W2113280143","https://openalex.org/W2124895386","https://openalex.org/W2125993726","https://openalex.org/W2152603800","https://openalex.org/W2603388381","https://openalex.org/W4242336842"],"related_works":["https://openalex.org/W1482551403","https://openalex.org/W1965191464","https://openalex.org/W1258892498","https://openalex.org/W2905073546","https://openalex.org/W2187958446","https://openalex.org/W2183579781","https://openalex.org/W3080158623","https://openalex.org/W2494517118","https://openalex.org/W4408470685","https://openalex.org/W2153879854"],"abstract_inverted_index":{"We":[0],"present":[1],"in":[2],"this":[3,35],"paper":[4],"a":[5,45],"code":[6],"for":[7,48],"the":[8,20,26,40,49],"class":[9,27,41],"of":[10,23,25,39],"unlabeled":[11],"split\u2013indifference":[12],"graphs.":[13],"This":[14],"codification":[15],"allows":[16],"us":[17],"to":[18,29,33],"establish":[19],"exact":[21],"number":[22],"elements":[24],"up":[28],"isomorphism.":[30],"In":[31],"order":[32],"obtain":[34],"result,":[36],"structural":[37],"properties":[38],"are":[42],"explored,":[43],"including":[44],"new":[46],"approach":[47],"characterization":[50],"theorem.":[51]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
