{"id":"https://openalex.org/W2148410650","doi":"https://doi.org/10.1137/0405048","title":"Labelling Graphs with a Condition at Distance 2","display_name":"Labelling Graphs with a Condition at Distance 2","publication_year":1992,"publication_date":"1992-11-01","ids":{"openalex":"https://openalex.org/W2148410650","doi":"https://doi.org/10.1137/0405048","mag":"2148410650"},"language":"en","primary_location":{"id":"doi:10.1137/0405048","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0405048","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/A5011011757","display_name":"Jerrold R. Griggs","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jerrold R. Griggs","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5109103096","display_name":"Roger K. Yeh","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Roger K. Yeh","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3782,"has_fulltext":false,"cited_by_count":722,"citation_normalized_percentile":{"value":0.82898825,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"5","issue":"4","first_page":"586","last_page":"595"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9997000098228455,"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":0.9997000098228455,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9973000288009644,"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":0.9972000122070312,"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":0.8719121813774109},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.7761974334716797},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6873089075088501},{"id":"https://openalex.org/keywords/simple-graph","display_name":"Simple graph","score":0.5837751626968384},{"id":"https://openalex.org/keywords/labelling","display_name":"Labelling","score":0.5680400133132935},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5105153322219849},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.42195719480514526},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3427608013153076},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1895577311515808},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10853853821754456}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8719121813774109},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.7761974334716797},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6873089075088501},{"id":"https://openalex.org/C2993105083","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Simple graph","level":3,"score":0.5837751626968384},{"id":"https://openalex.org/C2780523633","wikidata":"https://www.wikidata.org/wiki/Q380709","display_name":"Labelling","level":2,"score":0.5680400133132935},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5105153322219849},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.42195719480514526},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3427608013153076},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1895577311515808},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10853853821754456},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C73484699","wikidata":"https://www.wikidata.org/wiki/Q161733","display_name":"Criminology","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:10.1137/0405048","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0405048","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":11,"referenced_works":["https://openalex.org/W585470945","https://openalex.org/W1484040084","https://openalex.org/W1971367602","https://openalex.org/W1981159511","https://openalex.org/W2011039300","https://openalex.org/W2042077324","https://openalex.org/W2056979696","https://openalex.org/W2064102927","https://openalex.org/W2085716675","https://openalex.org/W2143474538","https://openalex.org/W2320198223"],"related_works":["https://openalex.org/W2951305269","https://openalex.org/W2897806428","https://openalex.org/W2391518723","https://openalex.org/W2010965931","https://openalex.org/W2805115653","https://openalex.org/W1996149838","https://openalex.org/W3014749936","https://openalex.org/W4205475737","https://openalex.org/W2364012696","https://openalex.org/W2622512907"],"abstract_inverted_index":{"Given":[0],"a":[1,10,22,201],"simple":[2],"graph":[3],"$G":[4],"=":[5,110,130,143,161],"(":[6,16,25,42,47,65,70,78,95,103,119,140,145,158,180,194,210],"V,E":[7],")$":[8,31,83,212],"and":[9,53,59,132],"positive":[11],"number":[12,87],"d,":[13],"an":[14,93],"$L_d":[15,77,94],"2,1":[17,79,96],")$-labelling":[18,80,97],"of":[19,151,154,175,224],"G":[20,26,91,141,181,190,195,211],"is":[21,61,84,113,135,170,191,213],"function":[23],"$f:V":[24],")":[27,44,49,67,72,142,160,182,196],"\\to":[28],"[":[29],"0,\\infty":[30],"such":[32,89],"that":[33,90,115,172],"whenever":[34,54],"$x,y":[35],"\\in":[36,107],"V$":[37],"are":[38,167],"adjacent,":[39],"$|":[40,63],"f":[41,46,64,69,98,102],"x":[43,58,66],"-":[45,68],"y":[48,60,71],"|":[50,73],"\\geq":[51,74],"2d$,":[52],"the":[55,85,126,133,222],"distance":[56],"between":[57],"two,":[62],"d$.":[75],"The":[76,148],"number$(":[81],"G,d":[82,120],"smallest":[86],"m":[88],"has":[92],"with":[99],"$\\max":[100],"\\{":[101],"v":[104,106],"):":[105],"V":[108],"\\}":[109],"m$.":[111],"It":[112,169],"shown":[114,171,214],"to":[116,124,215,221],"determine":[117],"$\\lambda":[118,139,157,209],")$,":[121],"it":[122,220],"suffices":[123],"study":[125],"case":[127],"when":[128],"$d":[129],"1$":[131],"labelling":[134,149],"nonnegative":[136],"integral-valued.":[137],"Let":[138],"\\lambda":[144],"G,1":[146],")$.":[147],"numbers":[150],"special":[152],"classes":[153],"graphs,":[155],"e.g.,":[156],"C":[159],"4$":[162],"for":[163,173,204],"any":[164],"cycle":[165],"C,":[166],"described.":[168],"graphs":[174],"maximum":[176],"degree":[177],"$\\Delta":[178,206],",\\lambda":[179],"\\leq":[183,197],"\\Delta":[184,198],"^2":[185,199],"+":[186],"2\\Delta":[187],"$.":[188,207],"If":[189],"diameter":[192],"$2,\\lambda":[193],"$,":[200],"sharp":[202],"bound":[203],"some":[205],"Determining":[208],"be":[216],"NP-complete":[217],"by":[218],"relating":[219],"problem":[223],"finding":[225],"Hamilton":[226],"paths.":[227]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":11},{"year":2024,"cited_by_count":25},{"year":2023,"cited_by_count":38},{"year":2022,"cited_by_count":27},{"year":2021,"cited_by_count":30},{"year":2020,"cited_by_count":23},{"year":2019,"cited_by_count":23},{"year":2018,"cited_by_count":24},{"year":2017,"cited_by_count":25},{"year":2016,"cited_by_count":21},{"year":2015,"cited_by_count":34},{"year":2014,"cited_by_count":40},{"year":2013,"cited_by_count":45},{"year":2012,"cited_by_count":49}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
