{"id":"https://openalex.org/W2021768304","doi":"https://doi.org/10.1016/0012-365x(87)90236-6","title":"A short proof and a strengthening of the Whitney 2-isomorphism theorem on graphs","display_name":"A short proof and a strengthening of the Whitney 2-isomorphism theorem on graphs","publication_year":1987,"publication_date":"1987-03-01","ids":{"openalex":"https://openalex.org/W2021768304","doi":"https://doi.org/10.1016/0012-365x(87)90236-6","mag":"2021768304"},"language":"en","primary_location":{"id":"doi:10.1016/0012-365x(87)90236-6","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0012-365x(87)90236-6","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete 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/A5044955882","display_name":"Alexander Kelmans","orcid":null},"institutions":[{"id":"https://openalex.org/I2800895607","display_name":"Space Research Institute","ror":"https://ror.org/04ryvdf08","country_code":"RU","type":"government","lineage":["https://openalex.org/I1313323035","https://openalex.org/I2800895607","https://openalex.org/I4210096333"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"A.K Kelmans","raw_affiliation_strings":["Profsouznaya 130-3-33, 117321 Moscow, U.S.S.R"],"affiliations":[{"raw_affiliation_string":"Profsouznaya 130-3-33, 117321 Moscow, U.S.S.R","institution_ids":["https://openalex.org/I2800895607"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5044955882"],"corresponding_institution_ids":["https://openalex.org/I2800895607"],"apc_list":{"value":3000,"currency":"USD","value_usd":3000},"apc_paid":null,"fwci":0.5325,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.61599603,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"64","issue":"1","first_page":"13","last_page":"25"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"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":0.9998999834060669,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9959999918937683,"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/mathematics","display_name":"Mathematics","score":0.9151583909988403},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.6584243774414062},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6537528038024902},{"id":"https://openalex.org/keywords/isomorphism-theorem","display_name":"Isomorphism theorem","score":0.5164085030555725},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4854589104652405}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9151583909988403},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.6584243774414062},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6537528038024902},{"id":"https://openalex.org/C26231708","wikidata":"https://www.wikidata.org/wiki/Q1065966","display_name":"Isomorphism theorem","level":2,"score":0.5164085030555725},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4854589104652405},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0},{"id":"https://openalex.org/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/0012-365x(87)90236-6","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0012-365x(87)90236-6","pdf_url":null,"source":{"id":"https://openalex.org/S18902827","display_name":"Discrete Mathematics","issn_l":"0012-365X","issn":["0012-365X","1872-681X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics","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":15,"referenced_works":["https://openalex.org/W1484040084","https://openalex.org/W1504925519","https://openalex.org/W1751782804","https://openalex.org/W1974936141","https://openalex.org/W1993421421","https://openalex.org/W1996335482","https://openalex.org/W2010142885","https://openalex.org/W2033240305","https://openalex.org/W2073730657","https://openalex.org/W2082076551","https://openalex.org/W2118628437","https://openalex.org/W4212859291","https://openalex.org/W4231597948","https://openalex.org/W4234391028","https://openalex.org/W4300303686"],"related_works":["https://openalex.org/W2389993406","https://openalex.org/W2382558759","https://openalex.org/W2384000006","https://openalex.org/W2300420233","https://openalex.org/W2964298956","https://openalex.org/W3212812839","https://openalex.org/W2129121083","https://openalex.org/W3011594387","https://openalex.org/W2039393591","https://openalex.org/W2354689617"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}