{"id":"https://openalex.org/W4233740959","doi":"https://doi.org/10.1002/jgt.1020","title":"Average distance in colored graphs","display_name":"Average distance in colored graphs","publication_year":2001,"publication_date":"2001-07-27","ids":{"openalex":"https://openalex.org/W4233740959","doi":"https://doi.org/10.1002/jgt.1020"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.1020","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-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/A5066897464","display_name":"Peter Dankelmann","orcid":"https://orcid.org/0000-0003-4376-7546"},"institutions":[{"id":"https://openalex.org/I95023434","display_name":"University of KwaZulu-Natal","ror":"https://ror.org/04qzfn040","country_code":"ZA","type":"funder","lineage":["https://openalex.org/I95023434"]}],"countries":["ZA"],"is_corresponding":false,"raw_author_name":"Peter Dankelmann","raw_affiliation_strings":["School of Mathematical and Statistical Sciences, University of Natal, Durban, 4041, South Africa"],"affiliations":[{"raw_affiliation_string":"School of Mathematical and Statistical Sciences, University of Natal, Durban, 4041, South Africa","institution_ids":["https://openalex.org/I95023434"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110056335","display_name":"Wayne Goddard","orcid":null},"institutions":[{"id":"https://openalex.org/I95023434","display_name":"University of KwaZulu-Natal","ror":"https://ror.org/04qzfn040","country_code":"ZA","type":"funder","lineage":["https://openalex.org/I95023434"]}],"countries":["ZA"],"is_corresponding":true,"raw_author_name":"Wayne Goddard","raw_affiliation_strings":["School of Geological and Computer Sciences, University of Natal, Durban, 4041, South Africa"],"affiliations":[{"raw_affiliation_string":"School of Geological and Computer Sciences, University of Natal, Durban, 4041, South Africa","institution_ids":["https://openalex.org/I95023434"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087896936","display_name":"Peter R. Slater","orcid":"https://orcid.org/0000-0002-6280-7673"},"institutions":[{"id":"https://openalex.org/I82495205","display_name":"University of Alabama in Huntsville","ror":"https://ror.org/02zsxwr40","country_code":"US","type":"funder","lineage":["https://openalex.org/I82495205"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Peter Slater","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Alabama in Huntsville, Huntsville Alabama 85899"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Alabama in Huntsville, Huntsville Alabama 85899","institution_ids":["https://openalex.org/I82495205"]}]}],"institution_assertions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5110056335"],"corresponding_institution_ids":["https://openalex.org/I95023434"],"apc_list":{"value":3760,"currency":"USD","value_usd":3760},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":3,"citation_normalized_percentile":{"value":0.521714,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":69,"max":72},"biblio":{"volume":"38","issue":"1","first_page":"1","last_page":"17"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9994,"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":0.9994,"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":0.9945,"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/T11502","display_name":"Facility Location and Emergency Management","score":0.9865,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/colored","display_name":"Colored","score":0.88825023}],"concepts":[{"id":"https://openalex.org/C2778307483","wikidata":"https://www.wikidata.org/wiki/Q5149038","display_name":"Colored","level":2,"score":0.88825023},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.87418246},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.80658567},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.52347267},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.44595742},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41398537},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.1020","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":6,"referenced_works":["https://openalex.org/W1996491085","https://openalex.org/W2011039300","https://openalex.org/W2069589129","https://openalex.org/W2603388381","https://openalex.org/W4237088952","https://openalex.org/W4244712399"],"related_works":["https://openalex.org/W891964471","https://openalex.org/W4284887816","https://openalex.org/W4235907447","https://openalex.org/W4205128724","https://openalex.org/W346008744","https://openalex.org/W3146178872","https://openalex.org/W2484916042","https://openalex.org/W2140509105","https://openalex.org/W2072835713","https://openalex.org/W2040849466"],"abstract_inverted_index":{"Abstract":[0],"For":[1],"a":[2,34,75,103],"graph":[3],"G":[4,14],"where":[5],"the":[6,10,18,21,46,58,80,95],"vertices":[7,28],"are":[8],"colored,":[9],"colored":[11,48],"distance":[12,49],"of":[13,20,27,38,60,83,88],"is":[15,43,98,102],"defined":[16,44],"as":[17,45],"sum":[19],"distances":[22],"between":[23],"all":[24,51],"unordered":[25],"pairs":[26],"having":[29],"different":[30],"colors.":[31],"Then":[32],"for":[33,106],"fixed":[35],"supply":[36],"s":[37,41,54],"colors,":[39],"d":[40],"(G)":[42],"minimum":[47],"over":[50],"colorings":[52],"with":[53],".":[55],"This":[56],"generalizes":[57],"concepts":[59],"median":[61],"and":[62,79,90],"average":[63],"distance.":[64],"In":[65],"this":[66,72],"paper":[67],"we":[68],"explore":[69],"bounds":[70],"on":[71],"parameter,":[73],"especially":[74],"natural":[76],"lower":[77],"bound":[78],"particular":[81],"case":[82],"balanced":[84],"2\u2010colorings":[85],"(equal":[86],"numbers":[87],"red":[89],"blue).":[91],"We":[92],"show":[93],"that":[94],"general":[96],"problem":[97],"NP\u2010hard":[99],"but":[100],"there":[101],"polynomial\u2010time":[104],"algorithm":[105],"trees.":[107],"\u00a9":[108],"2001":[109,120],"John":[110],"Wiley":[111],"&":[112],"Sons,":[113],"Inc.":[114],"J":[115],"Graph":[116],"Theory":[117],"38:":[118],"1\u201317,":[119]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W4233740959","counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-03-18T11:56:08.858887","created_date":"2022-05-12"}