{"id":"https://openalex.org/W2048591868","doi":"https://doi.org/10.1080/00207169508804359","title":"Invariants of E-graphs","display_name":"Invariants of E-graphs","publication_year":1995,"publication_date":"1995-01-01","ids":{"openalex":"https://openalex.org/W2048591868","doi":"https://doi.org/10.1080/00207169508804359","mag":"2048591868"},"language":"en","primary_location":{"id":"doi:10.1080/00207169508804359","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169508804359","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5070458571","display_name":"Teresa W. Haynes","orcid":"https://orcid.org/0000-0002-0865-0871"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Teresa W. Haynes","raw_affiliation_strings":["Department of Computer Science ,"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science ,","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072535201","display_name":"L. M. Lawson","orcid":null},"institutions":[{"id":"https://openalex.org/I119443389","display_name":"East Tennessee State University","ror":"https://ror.org/05rfqv493","country_code":"US","type":"education","lineage":["https://openalex.org/I119443389"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Linda M. Lawson","raw_affiliation_strings":["Department of Mathematics , East Tennessee State University , Johnson City, TN, 37614-0002"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , East Tennessee State University , Johnson City, TN, 37614-0002","institution_ids":["https://openalex.org/I119443389"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5070458571"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.18037392,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"55","issue":"1-2","first_page":"19","last_page":"27"},"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9987000226974487,"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":0.9854000210762024,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8003661036491394},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7814731597900391},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5335023403167725},{"id":"https://openalex.org/keywords/triangle-free-graph","display_name":"Triangle-free graph","score":0.5118264555931091},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.509204089641571},{"id":"https://openalex.org/keywords/indifference-graph","display_name":"Indifference graph","score":0.4810228943824768},{"id":"https://openalex.org/keywords/split-graph","display_name":"Split graph","score":0.46741318702697754},{"id":"https://openalex.org/keywords/windmill-graph","display_name":"Windmill graph","score":0.4494738280773163},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.4381028413772583},{"id":"https://openalex.org/keywords/cograph","display_name":"Cograph","score":0.435515820980072},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.41474583745002747},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.38368889689445496},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.30725574493408203},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.2659236490726471}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8003661036491394},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7814731597900391},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5335023403167725},{"id":"https://openalex.org/C114727528","wikidata":"https://www.wikidata.org/wiki/Q7840044","display_name":"Triangle-free graph","level":5,"score":0.5118264555931091},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.509204089641571},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.4810228943824768},{"id":"https://openalex.org/C8554925","wikidata":"https://www.wikidata.org/wiki/Q3893853","display_name":"Split graph","level":5,"score":0.46741318702697754},{"id":"https://openalex.org/C73380178","wikidata":"https://www.wikidata.org/wiki/Q8024306","display_name":"Windmill graph","level":5,"score":0.4494738280773163},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.4381028413772583},{"id":"https://openalex.org/C59824394","wikidata":"https://www.wikidata.org/wiki/Q5141281","display_name":"Cograph","level":5,"score":0.435515820980072},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.41474583745002747},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.38368889689445496},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.30725574493408203},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.2659236490726471}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00207169508804359","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169508804359","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:dc.etsu.edu:etsu-works-13068","is_oa":false,"landing_page_url":"https://dc.etsu.edu/etsu-works/11802","pdf_url":null,"source":{"id":"https://openalex.org/S4377196424","display_name":"Digital Commons - East Tennessee State University (East Tennessee State University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119443389","host_organization_name":"East Tennessee State University","host_organization_lineage":["https://openalex.org/I119443389"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ETSU Faculty Works","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W2054204410","https://openalex.org/W2058247779","https://openalex.org/W2069682869","https://openalex.org/W2161937309","https://openalex.org/W2799004609","https://openalex.org/W4213214460"],"related_works":["https://openalex.org/W1970985397","https://openalex.org/W2001877594","https://openalex.org/W1995451337","https://openalex.org/W2022743540","https://openalex.org/W1537900946","https://openalex.org/W2085219314","https://openalex.org/W3113980011","https://openalex.org/W2332903352","https://openalex.org/W2180968187","https://openalex.org/W1847712140","https://openalex.org/W2622748463","https://openalex.org/W1662147190","https://openalex.org/W1915707543","https://openalex.org/W2068725044","https://openalex.org/W2033128965","https://openalex.org/W1603416547","https://openalex.org/W1551410105","https://openalex.org/W2072854354","https://openalex.org/W2594144907","https://openalex.org/W43411129"],"abstract_inverted_index":{"An":[0,20],"E-graph":[1],"is":[2,25,68],"constructed":[3],"by":[4],"replacing":[5],"each":[6],"edge":[7,50,55],"in":[8],"a":[9,14,17],"core":[10],"graph":[11,18],"G":[12,39],"with":[13],"copy":[15],"of":[16,23,35,61,65],"H.":[19,41],"important":[21],"property":[22],"E-graphs":[24,67],"that":[26],"their":[27],"invariant":[28],"values":[29],"can":[30],"be":[31],"determined":[32],"from":[33],"parameters":[34],"the":[36],"original":[37],"graphs":[38],"and":[40,49,54,59],"We":[42],"determine":[43],"chromatic":[44],"number,":[45,47],"clique":[46],"vertex":[48,53],"cover":[51],"numbers,":[52,57],"independence":[56],"circumference,":[58],"girth":[60],"E-graphs.":[62],"A":[63],"characterization":[64],"hamiltonian":[66],"also":[69],"given.":[70]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}