{"id":"https://openalex.org/W2113910803","doi":"https://doi.org/10.1007/s00373-012-1191-x","title":"Neighbor Sum Distinguishing Index","display_name":"Neighbor Sum Distinguishing Index","publication_year":2012,"publication_date":"2012-05-25","ids":{"openalex":"https://openalex.org/W2113910803","doi":"https://doi.org/10.1007/s00373-012-1191-x","mag":"2113910803"},"language":"en","primary_location":{"id":"doi:10.1007/s00373-012-1191-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00373-012-1191-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00373-012-1191-x.pdf","source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graphs and Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00373-012-1191-x.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089946777","display_name":"Evelyne Flandrin","orcid":null},"institutions":[{"id":"https://openalex.org/I102197404","display_name":"Universit\u00e9 Paris-Sud","ror":"https://ror.org/028rypz17","country_code":"FR","type":"education","lineage":["https://openalex.org/I102197404"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Evelyne Flandrin","raw_affiliation_strings":["L R I, UMR 8623, B\u00e2t. 490, Universit\u00e9 de Paris-Sud, Orsay, France","Graphes, Algorithmes et Combinatoire (LRI)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"L R I, UMR 8623, B\u00e2t. 490, Universit\u00e9 de Paris-Sud, Orsay, France","institution_ids":["https://openalex.org/I102197404"]},{"raw_affiliation_string":"Graphes, Algorithmes et Combinatoire (LRI)","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025818275","display_name":"Antoni Marczyk","orcid":null},"institutions":[{"id":"https://openalex.org/I4210131439","display_name":"Applied Mathematics (United States)","ror":"https://ror.org/03seew607","country_code":"US","type":"company","lineage":["https://openalex.org/I4210131439"]},{"id":"https://openalex.org/I686019","display_name":"AGH University of Krakow","ror":"https://ror.org/00bas1c41","country_code":"PL","type":"education","lineage":["https://openalex.org/I686019"]}],"countries":["PL","US"],"is_corresponding":true,"raw_author_name":"Antoni Marczyk","raw_affiliation_strings":["AGH University of Science and Technology, Krakow, Poland","Faculty of Applied Mathematics [Krakow]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"AGH University of Science and Technology, Krakow, Poland","institution_ids":["https://openalex.org/I686019"]},{"raw_affiliation_string":"Faculty of Applied Mathematics [Krakow]","institution_ids":["https://openalex.org/I4210131439"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009715410","display_name":"Jakub Przyby\u0142o","orcid":"https://orcid.org/0000-0002-1262-7017"},"institutions":[{"id":"https://openalex.org/I686019","display_name":"AGH University of Krakow","ror":"https://ror.org/00bas1c41","country_code":"PL","type":"education","lineage":["https://openalex.org/I686019"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Jakub Przyby\u0142o","raw_affiliation_strings":["AGH University of Science and Technology, Krakow, Poland","AGH University of Science and Technology [Krakow, PL]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"AGH University of Science and Technology, Krakow, Poland","institution_ids":["https://openalex.org/I686019"]},{"raw_affiliation_string":"AGH University of Science and Technology [Krakow, PL]","institution_ids":["https://openalex.org/I686019"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059074776","display_name":"Jean-Fran\u00e7ois Sacl\u00e9","orcid":null},"institutions":[{"id":"https://openalex.org/I102197404","display_name":"Universit\u00e9 Paris-Sud","ror":"https://ror.org/028rypz17","country_code":"FR","type":"education","lineage":["https://openalex.org/I102197404"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jean-Fran\u00e7ois Sacl\u00e9","raw_affiliation_strings":["L R I, UMR 8623, B\u00e2t. 490, Universit\u00e9 de Paris-Sud, Orsay, France","Graphes, Algorithmes et Combinatoire (LRI)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"L R I, UMR 8623, B\u00e2t. 490, Universit\u00e9 de Paris-Sud, Orsay, France","institution_ids":["https://openalex.org/I102197404"]},{"raw_affiliation_string":"Graphes, Algorithmes et Combinatoire (LRI)","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085801031","display_name":"Mariusz Wo\u017aniak","orcid":"https://orcid.org/0000-0003-4769-0056"},"institutions":[{"id":"https://openalex.org/I686019","display_name":"AGH University of Krakow","ror":"https://ror.org/00bas1c41","country_code":"PL","type":"education","lineage":["https://openalex.org/I686019"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Mariusz Wo\u017aniak","raw_affiliation_strings":["AGH University of Science and Technology, Krakow, Poland","AGH University of Science and Technology [Krakow, PL]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"AGH University of Science and Technology, Krakow, Poland","institution_ids":["https://openalex.org/I686019"]},{"raw_affiliation_string":"AGH University of Science and Technology [Krakow, PL]","institution_ids":["https://openalex.org/I686019"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5025818275"],"corresponding_institution_ids":["https://openalex.org/I4210131439","https://openalex.org/I686019"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":{"value":2890,"currency":"USD","value_usd":2890},"fwci":5.4871,"has_fulltext":true,"cited_by_count":60,"citation_normalized_percentile":{"value":0.96367812,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"29","issue":"5","first_page":"1329","last_page":"1336"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","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/T12541","display_name":"Graph Labeling and Dimension Problems","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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.9127271175384521},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.780307948589325},{"id":"https://openalex.org/keywords/edge-coloring","display_name":"Edge coloring","score":0.6773993968963623},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6290587782859802},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5844173431396484},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3964987099170685},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.34444257616996765},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.16641104221343994}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.9127271175384521},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.780307948589325},{"id":"https://openalex.org/C123809776","wikidata":"https://www.wikidata.org/wiki/Q1050972","display_name":"Edge coloring","level":5,"score":0.6773993968963623},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6290587782859802},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5844173431396484},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3964987099170685},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.34444257616996765},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.16641104221343994}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00373-012-1191-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00373-012-1191-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00373-012-1191-x.pdf","source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graphs and Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-01753341v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01753341","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs00373-012-1191-x.pdf","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://link.springer.com/article/10.1007/s00373-012-1191-x#citeas","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s00373-012-1191-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00373-012-1191-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00373-012-1191-x.pdf","source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Graphs and Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2113910803.pdf","grobid_xml":"https://content.openalex.org/works/W2113910803.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W936019929","https://openalex.org/W1484040084","https://openalex.org/W2034742295","https://openalex.org/W2055120783","https://openalex.org/W2080071328","https://openalex.org/W2084488169","https://openalex.org/W2086863920"],"related_works":["https://openalex.org/W2949417215","https://openalex.org/W398688634","https://openalex.org/W4233059376","https://openalex.org/W4255910752","https://openalex.org/W2585997002","https://openalex.org/W2774090050","https://openalex.org/W2020575511","https://openalex.org/W4296859768","https://openalex.org/W2768840597","https://openalex.org/W4386742818"],"abstract_inverted_index":{"We":[0,104,113],"consider":[1],"proper":[2],"edge":[3],"colorings":[4],"of":[5,11,32,40,54,66,72,92,111],"a":[6,21,70],"graph":[7,87,122],"G":[8,73,88,123,133],"using":[9],"colors":[10,41,55],"the":[12,38,44,52,58,79],"set":[13],"{1,":[14],".":[15,16,17],",":[18],"k}.":[19],"Such":[20],"coloring":[22,71],"is":[23,49,74,134],"called":[24],"neighbor":[25],"sum":[26,39,53],"distinguishing":[27],"if":[28,132],"for":[29,84,108,120],"any":[30,85,121],"pair":[31],"adjacent":[33],"vertices":[34],"x":[35,48],"and":[36,128],"y":[37],"taken":[42,56],"on":[43,57],"edges":[45,59],"incident":[46,60],"to":[47,61],"different":[50],"from":[51],"y.":[62],"The":[63],"smallest":[64],"value":[65],"k":[67],"in":[68],"such":[69],"denoted":[75],"by":[76],"ndi\u03a3(G).":[77],"In":[78],"paper":[80],"we":[81,97],"conjecture":[82,107],"that":[83,116],"connected":[86],"\u2260":[89],"C":[90],"5":[91],"order":[93],"n":[94],"\u2265":[95,126],"3":[96],"have":[98],"ndi\u03a3(G)":[99,117,129],"\u2264":[100,118,130],"\u0394(G)":[101,125],"+":[102],"2.":[103],"prove":[105],"this":[106],"several":[109],"classes":[110],"graphs.":[112],"also":[114],"show":[115],"7\u0394(G)/2":[119],"with":[124],"2":[127],"8":[131],"cubic.":[135]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}