{"id":"https://openalex.org/W2085421834","doi":"https://doi.org/10.1137/s0895480193245339","title":"The $L(2,1)$-Labeling Problem on Graphs","display_name":"The $L(2,1)$-Labeling Problem on Graphs","publication_year":1996,"publication_date":"1996-05-01","ids":{"openalex":"https://openalex.org/W2085421834","doi":"https://doi.org/10.1137/s0895480193245339","mag":"2085421834"},"language":"en","primary_location":{"id":"doi:10.1137/s0895480193245339","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480193245339","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on 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/A5002508116","display_name":"Gerard J. Chang","orcid":null},"institutions":[{"id":"https://openalex.org/I148366613","display_name":"National Yang Ming Chiao Tung University","ror":"https://ror.org/00se2k293","country_code":"TW","type":"education","lineage":["https://openalex.org/I148366613"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Gerard J. Chang","raw_affiliation_strings":["National Chiao-Tung University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Chiao-Tung University","institution_ids":["https://openalex.org/I148366613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102124533","display_name":"David Kuo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"David Kuo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.086,"has_fulltext":false,"cited_by_count":371,"citation_normalized_percentile":{"value":0.94132653,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"9","issue":"2","first_page":"309","last_page":"316"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9995999932289124,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.9185508489608765},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.777843713760376},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.7387166023254395},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.5969903469085693},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5487684011459351},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5312283635139465},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4815535843372345},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3556249737739563},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1260237693786621}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.9185508489608765},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.777843713760376},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.7387166023254395},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.5969903469085693},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5487684011459351},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5312283635139465},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4815535843372345},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3556249737739563},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1260237693786621},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0895480193245339","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480193245339","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on 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":14,"referenced_works":["https://openalex.org/W1998152720","https://openalex.org/W2015906942","https://openalex.org/W2042077324","https://openalex.org/W2048357050","https://openalex.org/W2055841009","https://openalex.org/W2056979696","https://openalex.org/W2064102927","https://openalex.org/W2070694622","https://openalex.org/W2072141822","https://openalex.org/W2074820146","https://openalex.org/W2084535093","https://openalex.org/W2143474538","https://openalex.org/W2148410650","https://openalex.org/W2320198223"],"related_works":["https://openalex.org/W1964910584","https://openalex.org/W2059680011","https://openalex.org/W2905721092","https://openalex.org/W1527272374","https://openalex.org/W1974452921","https://openalex.org/W1719252778","https://openalex.org/W922283457","https://openalex.org/W1970195683","https://openalex.org/W2001841982","https://openalex.org/W2949706820"],"abstract_inverted_index":{"An":[0],"$L(2,1)$-labeling":[1,48,64],"of":[2,18,52,81,107],"a":[3,7,152,161],"graph":[4,105],"G":[5,53,61,106],"is":[6,54],"function":[8],"f":[9],"from":[10],"the":[11,16,55,116,133],"vertex":[12],"set":[13,17],"$V(G)$":[14],"to":[15,122,139,156],"all":[19],"nonnegative":[20],"integers":[21],"such":[22,59],"that":[23,60,94],"$|":[24,36],"f(x)":[25,37],"-":[26,38,147],"f(y)":[27,39],"|":[28,40],"\\geq":[29,41],"2$":[30],"if":[31,43],"$d(x,y)":[32,44],"=":[33,45,72],"1$":[34,42],"and":[35,86],"2$.":[46,148],"The":[47],"number":[49,57],"$\\lambda":[50,82,87,95,123,140,158],"(G)$":[51],"smallest":[56],"k":[58],"has":[62],"an":[63],"with":[65],"$\\max\\{":[66],"f(v":[67],"):v":[68],"\\in":[69],"V(G)":[70],"\\}":[71],"k$.":[73],"In":[74],"this":[75],"paper,":[76],"we":[77,150],"give":[78],"exact":[79],"formulas":[80],"(G":[83,88],"\\cup":[84],"H)$":[85],"+":[89,100,127,144],"H)$.":[90],"We":[91],"also":[92],"prove":[93],"(G)":[96,124,141,146],"\\leq":[97,125,142],"\\Delta":[98,101,143],"^2":[99],"$":[102],"for":[103,160],"any":[104],"maximum":[108],"degree":[109],"$\\Delta":[110],"$.":[111],"For":[112,129],"odd-sun-free":[113],"(OSF)-chordal":[114],"graphs,":[115,132],"upper":[117,134],"bound":[118,135],"can":[119,136],"be":[120,137],"reduced":[121,138],"2\\Delta":[126],"1$.":[128],"sun-free":[130],"(SF)-chordal":[131],"2\\chi":[145],"Finally,":[149],"present":[151],"polynomial":[153],"time":[154],"algorithm":[155],"determine":[157],"(T)$":[159],"tree":[162],"T.":[163]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":11},{"year":2015,"cited_by_count":16},{"year":2014,"cited_by_count":19},{"year":2013,"cited_by_count":17},{"year":2012,"cited_by_count":21}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}