{"id":"https://openalex.org/W2321742174","doi":"https://doi.org/10.1080/00207160.2015.1109640","title":"Trees with large numbers of subtrees","display_name":"Trees with large numbers of subtrees","publication_year":2015,"publication_date":"2015-10-20","ids":{"openalex":"https://openalex.org/W2321742174","doi":"https://doi.org/10.1080/00207160.2015.1109640","mag":"2321742174"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2015.1109640","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2015.1109640","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"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":"International Journal of Computer 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/A5023270649","display_name":"Yuzhi Xiao","orcid":"https://orcid.org/0000-0003-2086-0422"},"institutions":[{"id":"https://openalex.org/I20616075","display_name":"Qinghai Normal University","ror":"https://ror.org/03az1t892","country_code":"CN","type":"education","lineage":["https://openalex.org/I20616075"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuzhi Xiao","raw_affiliation_strings":[",","School of Computer, Qinghai Normal, University, Xining, Qinghai, China"],"affiliations":[{"raw_affiliation_string":",","institution_ids":[]},{"raw_affiliation_string":"School of Computer, Qinghai Normal, University, Xining, Qinghai, China","institution_ids":["https://openalex.org/I20616075"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078200110","display_name":"Haixing Zhao","orcid":"https://orcid.org/0000-0003-0957-1603"},"institutions":[{"id":"https://openalex.org/I20616075","display_name":"Qinghai Normal University","ror":"https://ror.org/03az1t892","country_code":"CN","type":"education","lineage":["https://openalex.org/I20616075"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Haixing Zhao","raw_affiliation_strings":[",","School of Computer, Qinghai Normal, University, Xining, Qinghai, China"],"affiliations":[{"raw_affiliation_string":",","institution_ids":[]},{"raw_affiliation_string":"School of Computer, Qinghai Normal, University, Xining, Qinghai, China","institution_ids":["https://openalex.org/I20616075"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003356618","display_name":"Zhen Liu","orcid":"https://orcid.org/0000-0002-8107-0929"},"institutions":[{"id":"https://openalex.org/I18894396","display_name":"Nagasaki Institute of Applied Science","ror":"https://ror.org/051smb947","country_code":"JP","type":"education","lineage":["https://openalex.org/I18894396"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Zhen Liu","raw_affiliation_strings":["Nagasaki Institute of Applied Science, Nagasaki, Japan"],"affiliations":[{"raw_affiliation_string":"Nagasaki Institute of Applied Science, Nagasaki, Japan","institution_ids":["https://openalex.org/I18894396"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103286474","display_name":"Yaping Mao","orcid":"https://orcid.org/0000-0001-9134-237X"},"institutions":[{"id":"https://openalex.org/I20616075","display_name":"Qinghai Normal University","ror":"https://ror.org/03az1t892","country_code":"CN","type":"education","lineage":["https://openalex.org/I20616075"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yaping Mao","raw_affiliation_strings":[",","Department of Mathematics, Qinghai Normal University, Xining, Qinghai, China"],"affiliations":[{"raw_affiliation_string":",","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics, Qinghai Normal University, Xining, Qinghai, China","institution_ids":["https://openalex.org/I20616075"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5078200110"],"corresponding_institution_ids":["https://openalex.org/I20616075"],"apc_list":null,"apc_paid":null,"fwci":0.5343,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.69564154,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"94","issue":"2","first_page":"372","last_page":"385"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.9986000061035156,"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":0.8324859142303467},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7859317660331726},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.4936889111995697},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.4652942419052124},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4549930989742279},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.44805335998535156}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8324859142303467},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7859317660331726},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4936889111995697},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.4652942419052124},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4549930989742279},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.44805335998535156}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2015.1109640","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2015.1109640","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"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":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Life in Land","score":0.4300000071525574,"id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1484040084","https://openalex.org/W1985851625","https://openalex.org/W1998411156","https://openalex.org/W2002459766","https://openalex.org/W2021043715","https://openalex.org/W2028431563","https://openalex.org/W2039079531","https://openalex.org/W2065282816","https://openalex.org/W2084227912","https://openalex.org/W2108608076","https://openalex.org/W2136753780","https://openalex.org/W2146138435","https://openalex.org/W2146620962","https://openalex.org/W2171458593","https://openalex.org/W2324102510","https://openalex.org/W2593779793","https://openalex.org/W2729689113","https://openalex.org/W2949912983","https://openalex.org/W4205631061"],"related_works":["https://openalex.org/W1719252778","https://openalex.org/W922283457","https://openalex.org/W2031098440","https://openalex.org/W4307385446","https://openalex.org/W2466894780","https://openalex.org/W3092119098","https://openalex.org/W2003008160","https://openalex.org/W2381713449","https://openalex.org/W2731724293","https://openalex.org/W2904724461"],"abstract_inverted_index":{"The":[0],"number":[1,29,47,66,82,100,114],"of":[2,12,30,40,48,59,67,83,91,101,115,117,124],"subtrees":[3,31,49,69,84,116],"in":[4,70,85],"a":[5,13,56,76],"graph":[6],"is":[7,23],"related":[8],"to":[9,79,111],"the":[10,43,51,65,81,89,98,113],"reliability":[11],"network":[14],"with":[15,27,45,97,127],"possible":[16],"vertex":[17],"failure":[18],"and":[19,73,87,94],"edge":[20],"failure.":[21],"It":[22],"known":[24],"that":[25],"networks":[26],"larger":[28],"would":[32],"be":[33],"more":[34],"reliable.":[35],"Therefore,":[36],"for":[37],"given":[38],"families":[39],"graphs,":[41],"determining":[42],"graphs":[44],"maximum":[46,99],"within":[50],"family":[52],"becomes":[53],"important.":[54],"For":[55],"tree":[57,90],"T":[58,86],"n":[60,96,125],"vertices,":[61],"let":[62],"F(T)":[63],"denote":[64],"all":[68,122],"T.":[71],"Yan":[72],"Yeh":[74],"gave":[75],"linear-time":[77],"algorithm":[78],"count":[80,112],"determined":[88],"diameter":[92],"d":[93],"order":[95],"subtrees.":[102],"In":[103],"this":[104],"paper,":[105],"we":[106],"present":[107],"two":[108],"recursive":[109],"relations":[110],"trees.":[118],"We":[119],"also":[120],"characterize":[121],"trees":[123],"vertices":[126],"5+n+2n\u22123\u2264F(T)\u22642n\u22121+n\u22121.":[128]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-01-22T23:29:09.771500","created_date":"2025-10-10T00:00:00"}
