{"id":"https://openalex.org/W2084274653","doi":"https://doi.org/10.1002/jgt.3190040105","title":"Genus of cartesian products of regular bipartite graphs","display_name":"Genus of cartesian products of regular bipartite graphs","publication_year":1980,"publication_date":"1980-03-01","ids":{"openalex":"https://openalex.org/W2084274653","doi":"https://doi.org/10.1002/jgt.3190040105","mag":"2084274653"},"language":"en","primary_location":{"id":"doi:10.1002/jgt.3190040105","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.3190040105","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","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/A5009207700","display_name":"Toma\u017e Pisanski","orcid":"https://orcid.org/0000-0002-1257-5376"},"institutions":[{"id":"https://openalex.org/I153976015","display_name":"University of Ljubljana","ror":"https://ror.org/05njb9z20","country_code":"SI","type":"education","lineage":["https://openalex.org/I153976015"]}],"countries":["SI"],"is_corresponding":true,"raw_author_name":"Toma\u017e Pisanski","raw_affiliation_strings":["University of Ljubljana"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Ljubljana","institution_ids":["https://openalex.org/I153976015"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5009207700"],"corresponding_institution_ids":["https://openalex.org/I153976015"],"apc_list":{"value":3760,"currency":"USD","value_usd":3760},"apc_paid":null,"fwci":2.8689,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.91879252,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"4","issue":"1","first_page":"31","last_page":"42"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9983000159263611,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9926000237464905,"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":0.8862955570220947},{"id":"https://openalex.org/keywords/cartesian-product","display_name":"Cartesian product","score":0.8373305797576904},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.816055178642273},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8104357123374939},{"id":"https://openalex.org/keywords/quadrilateral","display_name":"Quadrilateral","score":0.5992357730865479},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.5905693769454956},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.514298141002655},{"id":"https://openalex.org/keywords/complete-bipartite-graph","display_name":"Complete bipartite graph","score":0.4943420886993408},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.44911491870880127},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39539816975593567},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.050422996282577515},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.049257487058639526}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8862955570220947},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.8373305797576904},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.816055178642273},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8104357123374939},{"id":"https://openalex.org/C151756577","wikidata":"https://www.wikidata.org/wiki/Q36810","display_name":"Quadrilateral","level":3,"score":0.5992357730865479},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.5905693769454956},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.514298141002655},{"id":"https://openalex.org/C134119311","wikidata":"https://www.wikidata.org/wiki/Q913598","display_name":"Complete bipartite graph","level":4,"score":0.4943420886993408},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.44911491870880127},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39539816975593567},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.050422996282577515},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.049257487058639526},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/jgt.3190040105","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.3190040105","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310419","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231"},{"id":"https://openalex.org/F4320324592","display_name":"Univerza v Ljubljani","ror":"https://ror.org/05njb9z20"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1484040084","https://openalex.org/W1974896505","https://openalex.org/W1976369905","https://openalex.org/W1990034619","https://openalex.org/W1998391578","https://openalex.org/W2003576269","https://openalex.org/W2025311671","https://openalex.org/W2039699664","https://openalex.org/W2078845444","https://openalex.org/W2326237727","https://openalex.org/W2944987113","https://openalex.org/W4213214460","https://openalex.org/W4239303259","https://openalex.org/W4243663091"],"related_works":["https://openalex.org/W2091826982","https://openalex.org/W245205139","https://openalex.org/W4322716869","https://openalex.org/W2036057584","https://openalex.org/W2912814903","https://openalex.org/W2107875203","https://openalex.org/W3206528106","https://openalex.org/W2347854397","https://openalex.org/W4234658180","https://openalex.org/W4235849992"],"abstract_inverted_index":{"Abstract":[0],"Let":[1],"G(n,":[2,25],"d)":[3,26],"denote":[4],"a":[5,87,97,137],"connected":[6,110],"regular":[7],"bipartite":[8,111],"graph":[9,112],"on":[10],"2":[11,39,42,45,67,79],"n":[12,31,41,53],"vertices":[13],"and":[14,94,126],"of":[15,99,113],"degree":[16,115],"d.":[17],"It":[18,101],"is":[19,102,108,121],"proved":[20,104],"that":[21,60,105],"any":[22,109],"Cartesian":[23],"product":[24],"\u00d7":[27,37,47,49,133],"G":[28,38,50,107,132],"1":[29,32,35,64,76],"(":[30,40,52],",":[33,43,55,65,85,117],"d":[34,44,56,63,66,69,73,75,78,83],")":[36,46],"\u20db":[48,81],"m":[51,54,57,70,84,120,123,128,135],"),":[58],"such":[59],"max":[61],"{":[62],",\u2026,":[68],"}":[71],"\u2264":[72,74],"+":[77,80,82],"has":[86,136],"quadrilateral":[88,138],"embedding,":[89],"thereby":[90,95],"establishing":[91],"its":[92],"genus,":[93],"generalizing":[96],"result":[98],"White.":[100],"also":[103],"if":[106,118,127],"maximum":[114],"D":[116,130],"Q":[119,134],"the":[122],"\u2010cube":[124],"graph,":[125],"\u2265":[129],"then":[131],"embedding.":[139]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
