{"id":"https://openalex.org/W1972615509","doi":"https://doi.org/10.1137/0405012","title":"Pair Labelings of Graphs","display_name":"Pair Labelings of Graphs","publication_year":1992,"publication_date":"1992-02-01","ids":{"openalex":"https://openalex.org/W1972615509","doi":"https://doi.org/10.1137/0405012","mag":"1972615509"},"language":"en","primary_location":{"id":"doi:10.1137/0405012","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0405012","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/A5050436724","display_name":"David R. Guichard","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"David R. Guichard","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5078951033","display_name":"John W. Krussel","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"John W. Krussel","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5050436724"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.09389084,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"5","issue":"1","first_page":"144","last_page":"149"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9977999925613403,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9977999925613403,"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":0.9976999759674072,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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":0.8968523740768433},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8315674066543579},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.67885422706604},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6250052452087402},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5233996510505676},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.5192573070526123},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.48177143931388855},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4801563620567322}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8968523740768433},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8315674066543579},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.67885422706604},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6250052452087402},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5233996510505676},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.5192573070526123},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.48177143931388855},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4801563620567322},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0405012","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0405012","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":2,"referenced_works":["https://openalex.org/W2042077324","https://openalex.org/W2130738665"],"related_works":["https://openalex.org/W2117548279","https://openalex.org/W2070252991","https://openalex.org/W2807449856","https://openalex.org/W2941201715","https://openalex.org/W2025727968","https://openalex.org/W238211858","https://openalex.org/W2196131019","https://openalex.org/W2112041331","https://openalex.org/W2950817880","https://openalex.org/W3178681420"],"abstract_inverted_index":{"Given":[0],"a":[1,26],"graph":[2],"G":[3,22],"and":[4],"positive":[5],"integer":[6],"d,":[7],"the":[8,14,61],"pair-labeling":[9],"number":[10,63],"$r^*":[11,58],"(G,d)$":[12],"is":[13],"minimum":[15],"n":[16],"such":[17],"that":[18,39],"each":[19],"vertex":[20],"in":[21],"can":[23],"be":[24],"assigned":[25],"pair":[27],"of":[28,57,64],"numbers":[29,42],"from":[30],"$\\{":[31],"0,1,":[32],"\\cdots":[33],",n":[34],"-":[35],"1":[36],"\\}$":[37],"so":[38],"any":[40],"two":[41],"used":[43],"at":[44,49],"adjacent":[45],"vertices":[46],"differ":[47],"by":[48],"least":[50],"d":[51],"modulo":[52],"n.":[53],"All":[54],"possible":[55],"values":[56],"(G,d)$,":[59],"given":[60],"chromatic":[62],"G,":[65],"are":[66],"determined.":[67]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
