{"id":"https://openalex.org/W2143584297","doi":"https://doi.org/10.1080/15427951.2007.10129140","title":"Real Number Labelings for Paths and Cycles","display_name":"Real Number Labelings for Paths and Cycles","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2143584297","doi":"https://doi.org/10.1080/15427951.2007.10129140","mag":"2143584297"},"language":"en","primary_location":{"id":"doi:10.1080/15427951.2007.10129140","is_oa":true,"landing_page_url":"https://doi.org/10.1080/15427951.2007.10129140","pdf_url":"https://www.internetmathematicsjournal.com/article/1437.pdf","source":{"id":"https://openalex.org/S19474917","display_name":"Internet Mathematics","issn_l":"1542-7951","issn":["1542-7951","1944-9488"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Internet Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.internetmathematicsjournal.com/article/1437.pdf","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":0.7092,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.75343648,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"4","issue":"1","first_page":"65","last_page":"86"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9994000196456909,"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":0.9991999864578247,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8602476119995117},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7342769503593445},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5774103999137878},{"id":"https://openalex.org/keywords/real-number","display_name":"Real number","score":0.5562679767608643},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.4561459720134735},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45376670360565186},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.451452374458313},{"id":"https://openalex.org/keywords/infimum-and-supremum","display_name":"Infimum and supremum","score":0.42531338334083557},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09629151225090027}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8602476119995117},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7342769503593445},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5774103999137878},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.5562679767608643},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.4561459720134735},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45376670360565186},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.451452374458313},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.42531338334083557},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09629151225090027}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/15427951.2007.10129140","is_oa":true,"landing_page_url":"https://doi.org/10.1080/15427951.2007.10129140","pdf_url":"https://www.internetmathematicsjournal.com/article/1437.pdf","source":{"id":"https://openalex.org/S19474917","display_name":"Internet Mathematics","issn_l":"1542-7951","issn":["1542-7951","1944-9488"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Internet Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.im/1243430568","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.im/1243430568","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1080/15427951.2007.10129140","is_oa":true,"landing_page_url":"https://doi.org/10.1080/15427951.2007.10129140","pdf_url":"https://www.internetmathematicsjournal.com/article/1437.pdf","source":{"id":"https://openalex.org/S19474917","display_name":"Internet Mathematics","issn_l":"1542-7951","issn":["1542-7951","1944-9488"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Internet Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2143584297.pdf","grobid_xml":"https://content.openalex.org/works/W2143584297.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W2056979696","https://openalex.org/W2076840073","https://openalex.org/W2100446026","https://openalex.org/W2102310686","https://openalex.org/W2114385107","https://openalex.org/W2116612642","https://openalex.org/W2125158108","https://openalex.org/W2133847092","https://openalex.org/W2140515476","https://openalex.org/W2142803310","https://openalex.org/W2148410650"],"related_works":["https://openalex.org/W2102506430","https://openalex.org/W2364423979","https://openalex.org/W3182827720","https://openalex.org/W1596838019","https://openalex.org/W2133947431","https://openalex.org/W2490196280","https://openalex.org/W3208509670","https://openalex.org/W2275746642","https://openalex.org/W2100864966","https://openalex.org/W2109304297"],"abstract_inverted_index":{"The":[0,20],"problem":[1],"of":[2,9,26,47,63],"radio":[3],"channel":[4],"assignments":[5],"with":[6],"multiple":[7],"levels":[8],"interference":[10],"depending":[11],"on":[12],"distance":[13,81],"can":[14],"be":[15,112],"modelled":[16],"using":[17],"graph":[18,33],"theory.":[19],"authors":[21],"previously":[22],"introduced":[23],"a":[24,32,113],"model":[25],"labeling":[27],"by":[28,69,86],"real":[29,38,50],"numbers.":[30],"Given":[31],"_G_,":[34],"possibly":[35],"infinite,":[36],"and":[37,66,77,127],"numbers":[39,51],"_k_<sub>1</sub>,":[40,88],"_k_<sub>2</sub>":[41],"\u2265":[42,53,108],"0,":[43,109],"an":[44],"_L_(_k_<sub>1</sub>,":[45],"_k_<sub>2</sub>)-labeling":[46],"_G_":[48],"assigns":[49],"_\u0192_(_x_)":[52],"0":[54],"to":[55,100],"the":[56,61,90],"vertices":[57,64],"_x_,":[58],"such":[59,94],"that":[60],"labels":[62],"_u_":[65,76],"_v_":[67,78],"differ":[68],"at":[70,80],"least":[71],"_k_<sub>":[72],"<em>i</em>":[73],"</sub>":[74],"if":[75],"are":[79],"_i_":[82],"apart.":[83],"We":[84],"denote":[85],"\u03bb(_G_;":[87,102],"_k_<sub>2</sub>)":[89],"infimum":[91],"span":[92],"over":[93],"labelings":[95],"_\u0192_.":[96],"It":[97],"is":[98],"enough":[99],"determine":[101],"_k_,":[103],"1)":[104],"for":[105,124],"reals":[106],"_k_":[107],"which":[110],"will":[111],"continuous":[114],"nondecreasing":[115],"piecewise":[116],"linear":[117],"function.":[118],"Here":[119],"we":[120],"present":[121],"these":[122],"functions":[123],"paths,":[125],"cycles,":[126],"wheels.":[128]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}