{"id":"https://openalex.org/W1979964603","doi":"https://doi.org/10.1137/s0895480103429800","title":"On the Structure of Graphs with Non-Surjective <i>L</i>(2,1)-Labelings","display_name":"On the Structure of Graphs with Non-Surjective <i>L</i>(2,1)-Labelings","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W1979964603","doi":"https://doi.org/10.1137/s0895480103429800","mag":"1979964603"},"language":"en","primary_location":{"id":"doi:10.1137/s0895480103429800","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480103429800","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/A5068363764","display_name":"John P. Georges","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"John P. Georges","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5032348670","display_name":"David W. Mauro","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"David W. Mauro","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5068363764"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0541,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.75371337,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"19","issue":"1","first_page":"208","last_page":"223"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9991999864578247,"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":0.9991999864578247,"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":0.9986000061035156,"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":0.9925000071525574,"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":0.8752370476722717},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7586585283279419},{"id":"https://openalex.org/keywords/surjective-function","display_name":"Surjective function","score":0.7238008379936218},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.6642360091209412},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.498823881149292},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.48687925934791565},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.41202154755592346},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36058467626571655},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1745922863483429}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8752370476722717},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7586585283279419},{"id":"https://openalex.org/C119238805","wikidata":"https://www.wikidata.org/wiki/Q229102","display_name":"Surjective function","level":2,"score":0.7238008379936218},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.6642360091209412},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.498823881149292},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.48687925934791565},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.41202154755592346},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36058467626571655},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1745922863483429},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0895480103429800","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480103429800","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W165297640","https://openalex.org/W1971367602","https://openalex.org/W1991460317","https://openalex.org/W1995854302","https://openalex.org/W1998152720","https://openalex.org/W1998823220","https://openalex.org/W2056979696","https://openalex.org/W2058787498","https://openalex.org/W2064102927","https://openalex.org/W2067463837","https://openalex.org/W2070118295","https://openalex.org/W2070694622","https://openalex.org/W2074820146","https://openalex.org/W2085421834","https://openalex.org/W2148410650","https://openalex.org/W2169148120","https://openalex.org/W2296490710","https://openalex.org/W4230613046","https://openalex.org/W4250732241","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W3015672237","https://openalex.org/W4256653909","https://openalex.org/W2911989606","https://openalex.org/W1972989769","https://openalex.org/W3026958673","https://openalex.org/W2068180495","https://openalex.org/W2064732611","https://openalex.org/W3140259146","https://openalex.org/W2996462830","https://openalex.org/W172915128"],"abstract_inverted_index":{"For":[0,77],"a":[1,12,75,85,120],"graph":[2],"G,":[3],"an":[4,147],"L(2,1)-labeling":[5,69,122],"of":[6,50,62,87,99,104,135,146,153,170,196,203],"G":[7,63],"with":[8,70,155,206],"span":[9,58,71],"k":[10,115],"is":[11,64,73,84,94,109,127,191],"mapping":[13],"$L":[14],"\\rightarrow":[15],"\\{0,":[16],"1,":[17,46],"2,":[18,33],"\\ldots,":[19,81],"k\\}$":[20],"such":[21],"that":[22,162,184],"adjacent":[23],"vertices":[24,34],"are":[25,38],"assigned":[26,39],"integers":[27,40],"which":[28,41,117,174],"differ":[29,42],"by":[30,43],"at":[31,35,44],"least":[32,45],"distance":[36],"two":[37],"and":[47,54,67,90,112,137,141,181,210],"the":[48,97,113,133,144,151,168,194,197],"image":[49,98],"L":[51,88],"includes":[52],"0":[53],"k.":[55],"The":[56,101],"minimum":[57,102,114],"over":[59,106],"all":[60,107],"L(2,1)-labelings":[61],"denoted":[65,110,128],"$\\lambda(G)$,":[66],"each":[68],"$\\lambda(G)$":[72],"called":[74],"$\\lambda$-labeling.":[76],"$h":[78],"\\in":[79,176],"\\{1,":[80],"k-1\\}$,":[82],"h":[83,93],"hole":[86],"if":[89,92],"only":[91],"not":[95],"in":[96],"L.":[100],"number":[103],"holes":[105],"$\\lambda$-labelings":[108,154],"$\\rho(G)$,":[111],"for":[116,173],"there":[118],"exists":[119],"surjective":[121],"onto":[123],"{0,1,":[124],"...,":[125],"k}":[126],"$\\mu(G)$.":[129],"This":[130],"paper":[131],"extends":[132],"work":[134],"Fishburn":[136],"Roberts":[138],"on":[139,150],"$\\rho$":[140,156],"$\\mu$":[142],"through":[143],"investigation":[145],"equivalence":[148],"relation":[149],"set":[152],"holes.":[157],"In":[158],"particular,":[159],"we":[160,182,200],"establish":[161],"$\\rho":[163,175,207],"\\leq":[164,216,218],"\\Delta$.":[165,219],"We":[166],"analyze":[167],"structure":[169],"those":[171],"graphs":[172,205],"\\{":[177],"\\Delta-1,":[178],"\\Delta":[179],"\\}$,":[180],"show":[183],"$\\mu":[185],"=":[186,208],"\\lambda+":[187],"1$":[188],"whenever":[189],"$\\lambda$":[190],"less":[192],"than":[193],"order":[195,211],"graph.":[198],"Finally,":[199],"give":[201],"constructions":[202],"connected":[204],"\\Delta$":[209],"$t(\\Delta":[212],"+":[213],"1)$,":[214],"$1":[215],"t":[217]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}