{"id":"https://openalex.org/W2759695324","doi":"https://doi.org/10.3390/sym9100205","title":"\u03b2-Differential of a Graph","display_name":"\u03b2-Differential of a Graph","publication_year":2017,"publication_date":"2017-09-30","ids":{"openalex":"https://openalex.org/W2759695324","doi":"https://doi.org/10.3390/sym9100205","mag":"2759695324"},"language":"en","primary_location":{"id":"doi:10.3390/sym9100205","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym9100205","pdf_url":"https://www.mdpi.com/2073-8994/9/10/205/pdf?version=1508999594","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/9/10/205/pdf?version=1508999594","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033938960","display_name":"Ludwin A. Basilio","orcid":"https://orcid.org/0000-0001-5629-1343"},"institutions":[{"id":"https://openalex.org/I47400469","display_name":"Universidad Aut\u00f3noma de Zacatecas \"Francisco Garc\u00eda Salinas\"","ror":"https://ror.org/01m296r74","country_code":"MX","type":"education","lineage":["https://openalex.org/I47400469"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Ludwin Basilio","raw_affiliation_strings":["Academic Unit of Mathematics, Autonomous University of Zacatecas, Paseo la Bufa, int. Calzada Solidaridad, 98060 Zacatecas, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Academic Unit of Mathematics, Autonomous University of Zacatecas, Paseo la Bufa, int. Calzada Solidaridad, 98060 Zacatecas, Mexico","institution_ids":["https://openalex.org/I47400469"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052052405","display_name":"Sergio Bermudo","orcid":"https://orcid.org/0000-0003-4838-3170"},"institutions":[{"id":"https://openalex.org/I95013407","display_name":"Universidad Pablo de Olavide","ror":"https://ror.org/02z749649","country_code":"ES","type":"education","lineage":["https://openalex.org/I95013407"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Sergio Bermudo","raw_affiliation_strings":["Department of Economics, Quantitative Methods and Economic History, Pablo de Olavide University, Carretera de Utrera Km. 1, 41013 Sevilla, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Economics, Quantitative Methods and Economic History, Pablo de Olavide University, Carretera de Utrera Km. 1, 41013 Sevilla, Spain","institution_ids":["https://openalex.org/I95013407"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068318976","display_name":"Jes\u00fas Lea\u00f1os","orcid":"https://orcid.org/0000-0002-3441-8136"},"institutions":[{"id":"https://openalex.org/I47400469","display_name":"Universidad Aut\u00f3noma de Zacatecas \"Francisco Garc\u00eda Salinas\"","ror":"https://ror.org/01m296r74","country_code":"MX","type":"education","lineage":["https://openalex.org/I47400469"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Jes\u00fas Lea\u00f1os","raw_affiliation_strings":["Academic Unit of Mathematics, Autonomous University of Zacatecas, Paseo la Bufa, int. Calzada Solidaridad, 98060 Zacatecas, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Academic Unit of Mathematics, Autonomous University of Zacatecas, Paseo la Bufa, int. Calzada Solidaridad, 98060 Zacatecas, Mexico","institution_ids":["https://openalex.org/I47400469"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041892602","display_name":"Jos\u00e9 M. Sigarreta","orcid":"https://orcid.org/0000-0002-0863-4695"},"institutions":[{"id":"https://openalex.org/I3130105584","display_name":"Universidad Aut\u00f3noma de Guerrero","ror":"https://ror.org/054tbkd46","country_code":"MX","type":"education","lineage":["https://openalex.org/I3130105584"]}],"countries":["MX"],"is_corresponding":true,"raw_author_name":"Jos\u00e9 Sigarreta","raw_affiliation_strings":["Faculty of Mathematics, Autonomous University of Guerrero, Carlos E. Adame 5, Col. La Garita, 39350 Acapulco, Guerrero, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Autonomous University of Guerrero, Carlos E. Adame 5, Col. La Garita, 39350 Acapulco, Guerrero, Mexico","institution_ids":["https://openalex.org/I3130105584"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5041892602"],"corresponding_institution_ids":["https://openalex.org/I3130105584"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.7175,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.74051623,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"9","issue":"10","first_page":"205","last_page":"205"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9980999827384949,"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":0.9980999827384949,"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/T11476","display_name":"Graph theory and applications","score":0.9829999804496765,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9765999913215637,"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":0.762829065322876},{"id":"https://openalex.org/keywords/simple-graph","display_name":"Simple graph","score":0.6965488791465759},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6631970405578613},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.661927342414856},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6099226474761963},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.5532169938087463},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.45984944701194763},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4346140921115875},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.22972533106803894},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.06805586814880371}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.762829065322876},{"id":"https://openalex.org/C2993105083","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Simple graph","level":3,"score":0.6965488791465759},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6631970405578613},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.661927342414856},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6099226474761963},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.5532169938087463},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.45984944701194763},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4346140921115875},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.22972533106803894},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.06805586814880371},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym9100205","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym9100205","pdf_url":"https://www.mdpi.com/2073-8994/9/10/205/pdf?version=1508999594","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:c03aa27c0dfa42f2a0e3108e26a7bd25","is_oa":true,"landing_page_url":"https://doaj.org/article/c03aa27c0dfa42f2a0e3108e26a7bd25","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":"Symmetry, Vol 9, Iss 10, p 205 (2017)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/9/10/205/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym9100205","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym9100205","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym9100205","pdf_url":"https://www.mdpi.com/2073-8994/9/10/205/pdf?version=1508999594","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W118344247","https://openalex.org/W1654194294","https://openalex.org/W1971816016","https://openalex.org/W1988859742","https://openalex.org/W2003370404","https://openalex.org/W2040446810","https://openalex.org/W2042274748","https://openalex.org/W2054991375","https://openalex.org/W2059179208","https://openalex.org/W2061820396","https://openalex.org/W2070546874","https://openalex.org/W2083887440","https://openalex.org/W2331245033","https://openalex.org/W2520148815","https://openalex.org/W2572325465","https://openalex.org/W2755053059","https://openalex.org/W6732265724","https://openalex.org/W7046780705"],"related_works":["https://openalex.org/W4310825608","https://openalex.org/W2897806428","https://openalex.org/W2078517125","https://openalex.org/W2391518723","https://openalex.org/W4390414100","https://openalex.org/W3014749936","https://openalex.org/W2805115653","https://openalex.org/W1996149838","https://openalex.org/W4205475737","https://openalex.org/W2364012696"],"abstract_inverted_index":{"Let":[0,20],"G":[1,87,106,109],"=":[2],"(":[3,30,48,58,72,86,94,105,118],"V":[4,15,41,81,130],",":[5,97,100],"E":[6],")":[7,32,50,60,74,88,99,107,120],"be":[8,22,33],"a":[9,23],"simple":[10],"graph":[11],"with":[12],"vertex":[13],"set":[14,18,35],"and":[16,27],"edge":[17],"E.":[19],"D":[21,31,39,43,49,52,59,64,73,79,119,125,128],"subset":[24],"of":[25,36,38,51,70,89,108,114,147],"V,":[26],"let":[28],"B":[29,57,117],"the":[34,83,101,111,144],"neighbours":[37],"in":[40,139],"\u2216":[42],".":[44,66,132],"The":[45,67],"differential":[46,84],"\u2202":[47,71,85,103],"is":[53,82,110],"defined":[54],"as":[55],"|":[56,61,63,65,116,121,124,126],"\u2212":[62,95,122],"maximum":[68,112],"value":[69,113],"taken":[75],"over":[76],"all":[77],"subsets":[78],"\u2286":[80,129],"G.":[90,148],"For":[91],"\u03b2":[92,104,123,145],"\u2208":[93],"1":[96],"\u0394":[98],"\u03b2-differential":[102],"{":[115],":":[127],"}":[131],"Motivated":[133],"by":[134],"an":[135],"influential":[136],"maximization":[137],"problem,":[138],"this":[140],"paper":[141],"we":[142],"study":[143],"-differential":[146]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}