{"id":"https://openalex.org/W2133847092","doi":"https://doi.org/10.1137/s0895480105446708","title":"Real Number Graph Labellings with Distance Conditions","display_name":"Real Number Graph Labellings with Distance Conditions","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2133847092","doi":"https://doi.org/10.1137/s0895480105446708","mag":"2133847092"},"language":"en","primary_location":{"id":"doi:10.1137/s0895480105446708","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480105446708","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/A5041756893","display_name":"Xiaohua Jin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiaohua Teresa Jin","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":4.3255,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.94647038,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"20","issue":"2","first_page":"302","last_page":"327"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","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/T10374","display_name":"Advanced Graph Theory Research","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"}},{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9994999766349792,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9991000294685364,"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/mathematics","display_name":"Mathematics","score":0.7897218465805054},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7671419382095337},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7121754884719849},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6488951444625854},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5318253636360168},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5082387328147888},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4963551163673401},{"id":"https://openalex.org/keywords/span","display_name":"Span (engineering)","score":0.48164501786231995},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.4755101799964905}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7897218465805054},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7671419382095337},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7121754884719849},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6488951444625854},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5318253636360168},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5082387328147888},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4963551163673401},{"id":"https://openalex.org/C2778753569","wikidata":"https://www.wikidata.org/wiki/Q1960395","display_name":"Span (engineering)","level":2,"score":0.48164501786231995},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.4755101799964905},{"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/C147176958","wikidata":"https://www.wikidata.org/wiki/Q77590","display_name":"Civil engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0895480105446708","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480105446708","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":18,"referenced_works":["https://openalex.org/W1542956397","https://openalex.org/W1980962492","https://openalex.org/W1991098243","https://openalex.org/W1999453570","https://openalex.org/W2027160172","https://openalex.org/W2043190015","https://openalex.org/W2056979696","https://openalex.org/W2068859057","https://openalex.org/W2072651004","https://openalex.org/W2074820146","https://openalex.org/W2085421834","https://openalex.org/W2121862002","https://openalex.org/W2143584297","https://openalex.org/W2148410650","https://openalex.org/W2165875673","https://openalex.org/W2349209936","https://openalex.org/W4232151508","https://openalex.org/W4245278569"],"related_works":["https://openalex.org/W2766104912","https://openalex.org/W4298198176","https://openalex.org/W2982829914","https://openalex.org/W4300694038","https://openalex.org/W4300410646","https://openalex.org/W3201982285","https://openalex.org/W2085096159","https://openalex.org/W2619045485","https://openalex.org/W1989316102","https://openalex.org/W2952208190"],"abstract_inverted_index":{"The":[0,73],"theory":[1],"of":[2,5,37,95,101,126,167,178],"integer":[3],"$\\lambda$-labellings":[4],"a":[6,35,93,123,153],"graph,":[7,82],"introduced":[8],"by":[9,49,152],"Griggs":[10,15],"and":[11,16,71,129,159,170],"Yeh":[12],"[J.":[13],"R.":[14,17],"K.-C.":[18],"Yeh,":[19],"SIAM":[20],"J.":[21],"Discrete":[22],"Math.,":[23],"5":[24],"(1992),":[25],"pp.":[26],"586-595],":[27],"seeks":[28],"to":[29,66],"model":[30,65],"efficient":[31],"channel":[32],"assignments":[33],"for":[34,43,80,174],"network":[36],"transmitters.":[38],"To":[39],"prevent":[40],"interference,":[41],"labels":[42,70,103],"nearby":[44],"vertices":[45],"must":[46],"be":[47,150],"separated":[48],"specified":[50],"amounts":[51],"$k_i$":[52],"depending":[53,155],"on":[54,157],"the":[55,64,102,105,111,119,127,146,168,175],"distance":[56,185],"i,":[57],"$1\\le":[58],"i\\le":[59],"p$.":[60],"Here":[61],"we":[62,130,171],"expand":[63],"allow":[67],"real":[68],"number":[69],"separations.":[72],"main":[74],"finding":[75],"(\"D-Set":[76],"Theorem\")":[77],"is":[78,92,122,134,144],"that":[79,118,132,145],"any":[81],"possibly":[83],"infinite,":[84],"with":[85,137,181],"maximum":[86],"degree":[87],"at":[88,184],"most":[89],"$\\Delta$,":[90],"there":[91],"labelling":[94],"minimum":[96,120,176],"span":[97,121],"in":[98,164],"which":[99],"all":[100],"have":[104],"form":[106],"$\\sum_{i=1}^p":[107],"a_i":[108],"k_i$,":[109],"where":[110],"$a_i$'s":[112],"are":[113],"integers":[114],"$\\ge0$.":[115],"We":[116,161],"show":[117],"continuous":[124],"function":[125],"$k_i$'s,":[128],"conjecture":[131,143],"it":[133],"piecewise":[135],"linear":[136],"finitely":[138],"many":[139],"pieces.":[140],"Our":[141],"stronger":[142],"coefficients":[147],"$a_i$":[148],"can":[149],"bounded":[151],"constant":[154],"only":[156],"$\\Delta$":[158],"p.":[160],"offer":[162],"results":[163],"strong":[165],"support":[166],"conjectures,":[169],"give":[172],"formulas":[173],"spans":[177],"several":[179],"graphs":[180],"general":[182],"conditions":[183],"two.":[186]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"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"}
