{"id":"https://openalex.org/W3199269713","doi":"https://doi.org/10.1142/s0218195921500011","title":"What Graphs are 2-Dot Product Graphs?","display_name":"What Graphs are 2-Dot Product Graphs?","publication_year":2021,"publication_date":"2021-03-01","ids":{"openalex":"https://openalex.org/W3199269713","doi":"https://doi.org/10.1142/s0218195921500011","mag":"3199269713"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195921500011","pdf_url":null,"source":{"id":"https://openalex.org/S25827807","display_name":"International Journal of Computational Geometry & Applications","issn_l":"0218-1959","issn":["0218-1959","1793-6357"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://durham-repository.worktribe.com/preview/1243289/33653.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029365650","display_name":"Matthew Johnson","orcid":"https://orcid.org/0000-0002-7295-2663"},"institutions":[{"id":"https://openalex.org/I190082696","display_name":"Durham University","ror":"https://ror.org/01v29qb04","country_code":"GB","type":"funder","lineage":["https://openalex.org/I190082696"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Matthew Johnson","raw_affiliation_strings":["School of Engineering and Computer Sciences, Durham University, United Kingdom"],"affiliations":[{"raw_affiliation_string":"School of Engineering and Computer Sciences, Durham University, United Kingdom","institution_ids":["https://openalex.org/I190082696"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027487467","display_name":"Dani\u00ebl Paulusma","orcid":"https://orcid.org/0000-0001-5945-9287"},"institutions":[{"id":"https://openalex.org/I190082696","display_name":"Durham University","ror":"https://ror.org/01v29qb04","country_code":"GB","type":"funder","lineage":["https://openalex.org/I190082696"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Dani\u00ebl Paulusma","raw_affiliation_strings":["School of Engineering and Computer Sciences, Durham University, United Kingdom"],"affiliations":[{"raw_affiliation_string":"School of Engineering and Computer Sciences, Durham University, United Kingdom","institution_ids":["https://openalex.org/I190082696"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041371022","display_name":"Erik Jan van Leeuwen","orcid":"https://orcid.org/0000-0001-5240-7257"},"institutions":[{"id":"https://openalex.org/I193662353","display_name":"Utrecht University","ror":"https://ror.org/04pp8hn57","country_code":"NL","type":"funder","lineage":["https://openalex.org/I193662353"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Erik Jan van Leeuwen","raw_affiliation_strings":["Department of Information and Computing Sciences, Utrecht University, Utrecht, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Department of Information and Computing Sciences, Utrecht University, Utrecht, The Netherlands","institution_ids":["https://openalex.org/I193662353"]}]}],"institution_assertions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"fulltext_origin":"pdf","cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":0,"max":56},"biblio":{"volume":"31","issue":"01","first_page":"1","last_page":"16"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.999,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.999,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9934,"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/T11478","display_name":"Caching and Content Delivery","score":0.9809,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/dot-product","display_name":"Dot product","score":0.57142544}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7082025},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6453118},{"id":"https://openalex.org/C32900221","wikidata":"https://www.wikidata.org/wiki/Q181365","display_name":"Dot product","level":2,"score":0.57142544},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.46556118},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.45380288},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.43507886},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41223112},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06925672}],"mesh":[],"locations_count":7,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218195921500011","pdf_url":null,"source":{"id":"https://openalex.org/S25827807","display_name":"International Journal of Computational Geometry & Applications","issn_l":"0218-1959","issn":["0218-1959","1793-6357"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"https://dro.dur.ac.uk/33653/1/33653.pdf","pdf_url":"https://durham-repository.worktribe.com/preview/1243289/33653.pdf","source":{"id":"https://openalex.org/S4377196258","display_name":"Durham Research Online (Durham University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":false,"is_core":false,"host_organization":"https://openalex.org/I190082696","host_organization_name":"Durham University","host_organization_lineage":["https://openalex.org/I190082696"],"host_organization_lineage_names":["Durham University"],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false},{"is_oa":true,"landing_page_url":"https://durham-repository.worktribe.com/file/1243268/1/Accepted%20Journal%20Article","pdf_url":"https://durham-repository.worktribe.com/file/1243268/1/Accepted%20Journal%20Article","source":null,"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false},{"is_oa":true,"landing_page_url":"https://durham-repository.worktribe.com/file/1153656/1/Accepted%20Conference%20Proceeding","pdf_url":"https://durham-repository.worktribe.com/file/1153656/1/Accepted%20Conference%20Proceeding","source":null,"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"acceptedVersion","is_accepted":true,"is_published":false},{"is_oa":true,"landing_page_url":"https://dro.dur.ac.uk/16184/","pdf_url":"https://durham-repository.worktribe.com/preview/1153682/16184.pdf","source":{"id":"https://openalex.org/S4306400188","display_name":"Durham Research Online (Durham University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":false,"is_core":false,"host_organization":"https://openalex.org/I190082696","host_organization_name":"Durham University","host_organization_lineage":["https://openalex.org/I190082696"],"host_organization_lineage_names":["Durham University"],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"acceptedVersion","is_accepted":true,"is_published":false},{"is_oa":true,"landing_page_url":"https://hdl.handle.net/11858/00-001M-0000-002C-5393-3","pdf_url":"https://pure.mpg.de/pubman/item/item_2388285_1/component/file_2388284/arXiv%3A1511.05009.pdf","source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":["Max Planck Society"],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1511.05009","pdf_url":"https://arxiv.org/pdf/1511.05009","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://dro.dur.ac.uk/33653/1/33653.pdf","pdf_url":"https://durham-repository.worktribe.com/preview/1243289/33653.pdf","source":{"id":"https://openalex.org/S4377196258","display_name":"Durham Research Online (Durham University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":false,"is_core":false,"host_organization":"https://openalex.org/I190082696","host_organization_name":"Durham University","host_organization_lineage":["https://openalex.org/I190082696"],"host_organization_lineage_names":["Durham University"],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.44,"id":"https://metadata.un.org/sdg/10"}],"grants":[{"funder":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council","award_id":"EP/G043434/1"}],"datasets":[],"versions":[],"referenced_works_count":17,"referenced_works":["https://openalex.org/W1579049696","https://openalex.org/W1848620603","https://openalex.org/W1971048994","https://openalex.org/W1985061429","https://openalex.org/W1990495065","https://openalex.org/W2038080222","https://openalex.org/W2049605303","https://openalex.org/W2066459332","https://openalex.org/W2070497706","https://openalex.org/W2093308813","https://openalex.org/W2112681514","https://openalex.org/W2115124828","https://openalex.org/W2154454189","https://openalex.org/W2963645630","https://openalex.org/W4244426546","https://openalex.org/W4292408570","https://openalex.org/W639947448"],"related_works":["https://openalex.org/W4309875728","https://openalex.org/W4297458755","https://openalex.org/W4231483845","https://openalex.org/W2963755879","https://openalex.org/W2914876789","https://openalex.org/W2155593833","https://openalex.org/W2134021315","https://openalex.org/W2060094367","https://openalex.org/W2053694797","https://openalex.org/W1963975449"],"abstract_inverted_index":{"Let":[0],"[Formula:":[1,11,18,27,34,45,49,59,67,82,91,97,105,120,126],"see":[2,12,19,28,35,46,50,60,68,83,92,98,106,121,127],"text]":[3,29,36,47,51],"be":[4,74,90],"an":[5,40],"integer.":[6],"From":[7],"a":[8,17,32,81,133,141],"set":[9],"of":[10,104,113,135,143,146],"text]-dimensional":[13],"vectors,":[14],"we":[15,116],"obtain":[16],"text]-dot":[20,84,107,128],"product":[21,58,71,85,108,129],"graph":[22,86,114,138],"by":[23,38],"letting":[24],"each":[25],"vector":[26],"correspond":[30],"to":[31,76,89,132],"vertex":[33],"and":[37,48,53,123],"adding":[39],"edge":[41],"between":[42],"two":[43],"vertices":[44],"if":[52,55],"only":[54],"their":[56],"dot":[57],"text],":[61,122],"for":[62,94],"some":[63],"fixed,":[64],"positive":[65],"threshold":[66],"text].":[69,99],"Dot":[70],"graphs":[72,109,130],"can":[73],"used":[75],"model":[77],"social":[78],"networks.":[79],"Recognizing":[80],"is":[87],"known":[88,137],"text]-hard":[93],"all":[95],"fixed":[96],"To":[100],"understand":[101],"the":[102,111,118],"position":[103],"in":[110],"landscape":[112],"classes,":[115],"consider":[117],"case":[119],"investigate":[124],"how":[125],"relate":[131],"number":[134,142],"other":[136],"classes":[139,145],"including":[140],"well-known":[144],"intersection":[147],"graphs.":[148]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W3199269713","counts_by_year":[],"updated_date":"2025-03-26T09:27:03.767509","created_date":"2021-09-27"}