{"id":"https://openalex.org/W4241392716","doi":"https://doi.org/10.1002/(sici)1097-0118(200005)34:1<100::aid-jgt9>3.0.co;2-r","title":"Knot graphs","display_name":"Knot graphs","publication_year":2000,"publication_date":"2000-05-01","ids":{"openalex":"https://openalex.org/W4241392716","doi":"https://doi.org/10.1002/(sici)1097-0118(200005)34:1<100::aid-jgt9>3.0.co;2-r"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1097-0118(200005)34:1<100::aid-jgt9>3.0.co;2-r","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0118(200005)34:1<100::aid-jgt9>3.0.co;2-r","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/A5064835526","display_name":"Steven D. Noble","orcid":"https://orcid.org/0000-0002-1621-0059"},"institutions":[{"id":"https://openalex.org/I59433898","display_name":"Brunel University of London","ror":"https://ror.org/00dn4t376","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I59433898"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"S. D. Noble","raw_affiliation_strings":["Department of Mathematical Sciences, Brunel University, Kingston Lane, Uxbridge UB8 3PH, United Kingdom"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Brunel University, Kingston Lane, Uxbridge UB8 3PH, United Kingdom","institution_ids":["https://openalex.org/I59433898"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090914315","display_name":"Dominic Welsh","orcid":"https://orcid.org/0000-0003-1750-219X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"D. J. A. Welsh","raw_affiliation_strings":["Mathematical Institute, 24-29 St. Giles, Oxford OX1 3LB, United Kingdom"],"affiliations":[{"raw_affiliation_string":"Mathematical Institute, 24-29 St. Giles, Oxford OX1 3LB, United Kingdom","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5064835526","https://openalex.org/A5090914315"],"corresponding_institution_ids":["https://openalex.org/I59433898"],"apc_list":{"value":3760,"currency":"USD","value_usd":3760},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.38027152,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"34","issue":"1","first_page":"100","last_page":"111"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9980999827384949,"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"}},"topics":[{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9980999827384949,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.996399998664856,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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":0.8120547533035278},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6904975175857544},{"id":"https://openalex.org/keywords/knot","display_name":"Knot (papermaking)","score":0.5681273341178894}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8120547533035278},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6904975175857544},{"id":"https://openalex.org/C2779863119","wikidata":"https://www.wikidata.org/wiki/Q6423048","display_name":"Knot (papermaking)","level":2,"score":0.5681273341178894},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C42360764","wikidata":"https://www.wikidata.org/wiki/Q83588","display_name":"Chemical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/(sici)1097-0118(200005)34:1<100::aid-jgt9>3.0.co;2-r","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0118(200005)34:1<100::aid-jgt9>3.0.co;2-r","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":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W134472367","https://openalex.org/W2039763834","https://openalex.org/W2133388875","https://openalex.org/W2171018259","https://openalex.org/W4213257303"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2042127053","https://openalex.org/W2142036596","https://openalex.org/W4238204885"],"abstract_inverted_index":{"We":[0,42,57],"consider":[1],"the":[2,9,13,45,52,60,63,66],"equivalence":[3],"classes":[4],"of":[5,12,28,47,54,62,65,76],"graphs":[6,49],"induced":[7],"by":[8,24],"unsigned":[10],"versions":[11],"Reidemeister":[14],"moves":[15],"on":[16],"knot":[17,40,48],"diagrams.":[18],"Any":[19],"graph":[20,33],"that":[21,44,59],"is":[22,37,71],"reducible":[23],"some":[25],"finite":[26],"sequence":[27],"these":[29,77],"moves,":[30],"to":[31],"a":[32,39],"with":[34],"no":[35],"edges,":[36],"called":[38],"graph.":[41],"show":[43],"class":[46],"strictly":[50],"contains":[51],"set":[53],"delta-wye":[55],"graphs.":[56],"prove":[58],"dimension":[61],"intersection":[64],"cycle":[67],"and":[68],"cocycle":[69],"spaces":[70],"an":[72],"effective":[73],"numerical":[74],"invariant":[75],"classes.":[78],"\u00a9":[79],"2000":[80,91],"John":[81],"Wiley":[82],"&":[83],"Sons,":[84],"Inc.":[85],"J":[86],"Graph":[87],"Theory":[88],"34:":[89],"100\u2013111,":[90]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2022-05-12T00:00:00"}
