{"id":"https://openalex.org/W2137393438","doi":"https://doi.org/10.1109/bmei.2009.5304812","title":"A Note on the Definition of a Tree","display_name":"A Note on the Definition of a Tree","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2137393438","doi":"https://doi.org/10.1109/bmei.2009.5304812","mag":"2137393438"},"language":"en","primary_location":{"id":"doi:10.1109/bmei.2009.5304812","is_oa":false,"landing_page_url":"https://doi.org/10.1109/bmei.2009.5304812","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 2nd International Conference on Biomedical Engineering and Informatics","raw_type":"proceedings-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/A5101458443","display_name":"Yao Ming","orcid":"https://orcid.org/0000-0002-6377-6063"},"institutions":[{"id":"https://openalex.org/I4210129425","display_name":"Lanzhou Petrochemical Polytechnic","ror":"https://ror.org/03pkj2z67","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210129425"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ming Yao","raw_affiliation_strings":["Department of Information Process and Control Engineering, Lanzhou Petrochemical College of Vocational Technology, Lanzhou, China","Dept. of Inf. Process & Control Eng., Lanzhou Petrochem. Coll. of Vocational Technol., Lanzhou, China"],"affiliations":[{"raw_affiliation_string":"Department of Information Process and Control Engineering, Lanzhou Petrochemical College of Vocational Technology, Lanzhou, China","institution_ids":["https://openalex.org/I4210129425"]},{"raw_affiliation_string":"Dept. of Inf. Process & Control Eng., Lanzhou Petrochem. Coll. of Vocational Technol., Lanzhou, China","institution_ids":["https://openalex.org/I4210129425"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101729321","display_name":"Bing Yao","orcid":"https://orcid.org/0000-0002-5416-5180"},"institutions":[{"id":"https://openalex.org/I68986083","display_name":"Northwest Normal University","ror":"https://ror.org/00gx3j908","country_code":"CN","type":"education","lineage":["https://openalex.org/I68986083"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bing Yao","raw_affiliation_strings":["College of Mathematics and Information Science, Northwest Normal University, Lanzhou, China","Coll. of Math. & Inf. Sci., Northwest Normal Univ., Lanzhou, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Information Science, Northwest Normal University, Lanzhou, China","institution_ids":["https://openalex.org/I68986083"]},{"raw_affiliation_string":"Coll. of Math. & Inf. Sci., Northwest Normal Univ., Lanzhou, China","institution_ids":["https://openalex.org/I68986083"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101458443"],"corresponding_institution_ids":["https://openalex.org/I4210129425"],"apc_list":null,"apc_paid":null,"fwci":0.3428,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.63355062,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"5"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9997000098228455,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9997000098228455,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9972000122070312,"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/T11708","display_name":"Photochromic and Fluorescence Chemistry","score":0.9351000189781189,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.6059793829917908},{"id":"https://openalex.org/keywords/tree-traversal","display_name":"Tree traversal","score":0.5816221833229065},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5301424264907837},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.49380478262901306},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4512839913368225},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3755389451980591},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.327905535697937},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.30656740069389343},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2979903817176819}],"concepts":[{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.6059793829917908},{"id":"https://openalex.org/C140745168","wikidata":"https://www.wikidata.org/wiki/Q1210082","display_name":"Tree traversal","level":2,"score":0.5816221833229065},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5301424264907837},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.49380478262901306},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4512839913368225},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3755389451980591},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.327905535697937},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30656740069389343},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2979903817176819}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/bmei.2009.5304812","is_oa":false,"landing_page_url":"https://doi.org/10.1109/bmei.2009.5304812","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 2nd International Conference on Biomedical Engineering and Informatics","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W55191700","https://openalex.org/W1484040084","https://openalex.org/W2112641412"],"related_works":["https://openalex.org/W2000144448","https://openalex.org/W2024593554","https://openalex.org/W3003396734","https://openalex.org/W2071261821","https://openalex.org/W67037240","https://openalex.org/W1978699240","https://openalex.org/W2067133893","https://openalex.org/W2287003313","https://openalex.org/W1975886103","https://openalex.org/W2950502167"],"abstract_inverted_index":{"Very":[0],"often":[1,11],"trees":[2,34],"appear":[3],"in":[4,13,52,59],"computer":[5],"science.":[6],"For":[7],"example,":[8],"information":[9],"is":[10,71,99],"stored":[12],"treelike":[14],"data":[15],"structures":[16],"and":[17,75,117],"the":[18,60,100,118],"execution":[19],"of":[20,30,102,104,107,121,123],"many":[21,40],"recursive":[22],"programs":[23],"can":[24,128],"be":[25,129],"regarded":[26],"as":[27,131],"a":[28,31,53,67,72,124],"traversal":[29],"tree.":[32],"Moreover,":[33],"are":[35,45],"efficiently":[36],"used":[37],"to":[38,111],"verify":[39],"very":[41],"difficult":[42],"problems":[43],"which":[44],"still":[46],"open":[47],"now.":[48],"As":[49],"known,":[50],"leaves":[51],"tree":[54,62,73],"play":[55],"an":[56],"important":[57],"role":[58],"Steiner":[61],"problem.":[63],"We":[64],"show":[65],"that":[66],"connected":[68],"graph":[69,126],"G":[70,108,127],"if":[74,77],"only":[76],"n":[78,94],"<sub":[79,85,89,95,138,144],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[80,86,90,96,139,145],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sub>":[81],"(G)":[82],"=":[83,133],"2+Sigma":[84],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">dges3</sub>":[87,140],"(d-2)n":[88],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">d</sub>":[91,146],"(G),":[92],"where":[93],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">i</sub>":[97],"G)":[98],"number":[101,119],"vertices":[103],"degree":[105],"i":[106,114],"with":[109],"respect":[110],"delta(G)":[112],"les":[113,115],"Delta(G),":[116],"phi(G)":[120,132],"faces":[122],"planar":[125],"expressed":[130],"2":[134],"+":[135],"1/2":[136],"Sigma":[137],"(d":[141],"-":[142],"2)n":[143],"(G).":[147]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
