{"id":"https://openalex.org/W2974244310","doi":"https://doi.org/10.1142/s1793830919500678","title":"Extremal trees with respect to the Steiner Wiener index","display_name":"Extremal trees with respect to the Steiner Wiener index","publication_year":2019,"publication_date":"2019-09-18","ids":{"openalex":"https://openalex.org/W2974244310","doi":"https://doi.org/10.1142/s1793830919500678","mag":"2974244310"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830919500678","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830919500678","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","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/A5100436760","display_name":"Jie Zhang","orcid":"https://orcid.org/0000-0002-5348-7671"},"institutions":[{"id":"https://openalex.org/I146613903","display_name":"Shanghai Lixin University of Accounting and Finance","ror":"https://ror.org/02g81yf77","country_code":"CN","type":"education","lineage":["https://openalex.org/I146613903"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jie Zhang","raw_affiliation_strings":["School of Insurance, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Insurance, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, P. R. China","institution_ids":["https://openalex.org/I146613903"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100602615","display_name":"Guangjun Zhang","orcid":"https://orcid.org/0000-0003-1365-716X"},"institutions":[{"id":"https://openalex.org/I143413998","display_name":"Qingdao University of Science and Technology","ror":"https://ror.org/041j8js14","country_code":"CN","type":"education","lineage":["https://openalex.org/I143413998"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guang-Jun Zhang","raw_affiliation_strings":["School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, P. R. China","institution_ids":["https://openalex.org/I143413998"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100403973","display_name":"Hua Wang","orcid":"https://orcid.org/0000-0002-9070-5383"},"institutions":[{"id":"https://openalex.org/I39815113","display_name":"Georgia Southern University","ror":"https://ror.org/04agmb972","country_code":"US","type":"education","lineage":["https://openalex.org/I39815113"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hua Wang","raw_affiliation_strings":["Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA 30460, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA 30460, USA","institution_ids":["https://openalex.org/I39815113"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100376227","display_name":"Xiao\u2010Dong Zhang","orcid":"https://orcid.org/0000-0003-0783-051X"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiao-Dong Zhang","raw_affiliation_strings":["School of Mathematical Sciences, MOE-LSC and SHL-MAC, Shanghai Jiao Tong University, 800 Dongchuan road, Shanghai, 200240, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, MOE-LSC and SHL-MAC, Shanghai Jiao Tong University, 800 Dongchuan road, Shanghai, 200240, P. R. China","institution_ids":["https://openalex.org/I183067930"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100436760"],"corresponding_institution_ids":["https://openalex.org/I146613903"],"apc_list":null,"apc_paid":null,"fwci":2.6594,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.90207457,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"11","issue":"06","first_page":"1950067","last_page":"1950067"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":1.0,"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":1.0,"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/T10211","display_name":"Computational Drug Discovery Methods","score":0.9950000047683716,"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/T10353","display_name":"Zeolite Catalysis and Synthesis","score":0.9685999751091003,"subfield":{"id":"https://openalex.org/subfields/1604","display_name":"Inorganic Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/wiener-index","display_name":"Wiener index","score":0.9175956845283508},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8517341017723083},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7485390305519104},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6218239665031433},{"id":"https://openalex.org/keywords/steiner-tree-problem","display_name":"Steiner tree problem","score":0.5982393026351929},{"id":"https://openalex.org/keywords/index","display_name":"Index (typography)","score":0.5526484251022339},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5277405977249146},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.4732537865638733},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4525349736213684},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43819770216941833},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.41558361053466797},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.41256946325302124},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10481724143028259},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0959644615650177},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07462263107299805},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.062264710664749146}],"concepts":[{"id":"https://openalex.org/C16640446","wikidata":"https://www.wikidata.org/wiki/Q909065","display_name":"Wiener index","level":3,"score":0.9175956845283508},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8517341017723083},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7485390305519104},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6218239665031433},{"id":"https://openalex.org/C76220878","wikidata":"https://www.wikidata.org/wiki/Q1764144","display_name":"Steiner tree problem","level":2,"score":0.5982393026351929},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.5526484251022339},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5277405977249146},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.4732537865638733},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4525349736213684},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43819770216941833},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.41558361053466797},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.41256946325302124},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10481724143028259},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0959644615650177},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07462263107299805},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.062264710664749146},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830919500678","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830919500678","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5233446276","display_name":null,"funder_award_id":"11801371","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6317899841","display_name":null,"funder_award_id":"11701372","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G736147581","display_name":null,"funder_award_id":"11971311","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8353878891","display_name":null,"funder_award_id":"16ZR1422400","funder_id":"https://openalex.org/F4320309612","funder_display_name":"Natural Science Foundation of Shanghai"},{"id":"https://openalex.org/G8381071902","display_name":null,"funder_award_id":"11531001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320309612","display_name":"Natural Science Foundation of Shanghai","ror":null},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W74903757","https://openalex.org/W1985851625","https://openalex.org/W2039011891","https://openalex.org/W2060659106","https://openalex.org/W2088641991","https://openalex.org/W2091691071","https://openalex.org/W2110782579","https://openalex.org/W2119196129","https://openalex.org/W2154892580","https://openalex.org/W2298803128","https://openalex.org/W2312328781","https://openalex.org/W2318794083","https://openalex.org/W2331428586","https://openalex.org/W2505436561","https://openalex.org/W2518534328","https://openalex.org/W2563289603","https://openalex.org/W2726724467","https://openalex.org/W2776184136","https://openalex.org/W2796184364","https://openalex.org/W4243709834"],"related_works":["https://openalex.org/W2118320476","https://openalex.org/W2161182859","https://openalex.org/W2025658531","https://openalex.org/W1503036335","https://openalex.org/W4244816249","https://openalex.org/W2115973883","https://openalex.org/W2739242419","https://openalex.org/W1585318792","https://openalex.org/W59641357","https://openalex.org/W28092394"],"abstract_inverted_index":{"The":[0],"well-known":[1],"Wiener":[2,30,35,72,89,113,125,175],"index":[3,73,90,126,176],"is":[4,83],"defined":[5],"as":[6,108],"the":[7,29,33,38,57,64,70,87,99,106,111,118,122,136,161,168,173],"sum":[8,39],"of":[9,28,40,43,56,76,121,129,186],"pairwise":[10],"distances":[11],"between":[12],"vertices.":[13,61],"Extremal":[14],"problems":[15,66],"with":[16,67,179],"respect":[17,68],"to":[18,69],"it":[19,82],"have":[20],"been":[21],"extensively":[22],"studied":[23],"for":[24,110,151],"trees.":[25,139,153],"A":[26],"generalization":[27],"index,":[31,36],"called":[32],"Steiner":[34,71,88,124,174],"takes":[37],"minimum":[41],"sizes":[42],"subgraphs":[44],"that":[45,109,171],"span":[46],"[Formula:":[47,58],"see":[48,59],"text]":[49,60],"given":[50,78,131,181],"vertices":[51],"over":[52],"all":[53],"possible":[54],"choices":[55],"We":[62,115,154],"consider":[63,117],"extremal":[65,100,138,169],"among":[74,127,177],"trees":[75,128,170,178],"a":[77,95,130,157,180],"degree":[79,132,183],"sequence.":[80],"First,":[81],"pointed":[84],"out":[85],"minimizing":[86],"in":[91],"general":[92,123],"may":[93,102],"be":[94,105],"difficult":[96],"problem,":[97],"although":[98],"structure":[101],"very":[103],"likely":[104],"same":[107],"regular":[112],"index.":[114],"then":[116],"upper":[119],"bound":[120],"sequence":[133],"and":[134,146],"study":[135],"corresponding":[137],"With":[140],"these":[141],"findings,":[142],"some":[143],"further":[144],"discussion":[145],"computational":[147,162],"analysis":[148],"are":[149],"presented":[150],"chemical":[152],"also":[155],"propose":[156],"conjecture":[158],"based":[159],"on":[160],"results.":[163],"In":[164],"addition,":[165],"we":[166],"identify":[167],"maximize":[172],"maximum":[182],"or":[184],"number":[185],"leaves.":[187]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}