{"id":"https://openalex.org/W2115626424","doi":"https://doi.org/10.1142/s1793830911000973","title":"THE HYPER-WIENER INDEX OF THE k<font>th</font> POWER OF A GRAPH","display_name":"THE HYPER-WIENER INDEX OF THE k<font>th</font> POWER OF A GRAPH","publication_year":2011,"publication_date":"2011-03-01","ids":{"openalex":"https://openalex.org/W2115626424","doi":"https://doi.org/10.1142/s1793830911000973","mag":"2115626424"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830911000973","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830911000973","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/A5014477100","display_name":"Weijuan Zhang","orcid":"https://orcid.org/0000-0003-3494-3114"},"institutions":[{"id":"https://openalex.org/I1334729051","display_name":"Xinjiang Normal University","ror":"https://ror.org/00ndrvk93","country_code":"CN","type":"education","lineage":["https://openalex.org/I1334729051"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"WEIJUAN ZHANG","raw_affiliation_strings":["School of Mathematical Sciences, Xinjiang Normal University, Urumqi, Xinjiang 830054, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Xinjiang Normal University, Urumqi, Xinjiang 830054, China","institution_ids":["https://openalex.org/I1334729051"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052810463","display_name":"Baoyindureng Wu","orcid":"https://orcid.org/0000-0001-7164-3116"},"institutions":[{"id":"https://openalex.org/I96908189","display_name":"Xinjiang University","ror":"https://ror.org/059gw8r13","country_code":"CN","type":"education","lineage":["https://openalex.org/I96908189"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"BAOYINDURENG WU","raw_affiliation_strings":["College of Mathematics and System Science, Xinjiang University, Urumqi, Xinjiang 830046, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and System Science, Xinjiang University, Urumqi, Xinjiang 830046, China","institution_ids":["https://openalex.org/I96908189"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015624868","display_name":"Xinhui An","orcid":"https://orcid.org/0000-0003-2048-0497"},"institutions":[{"id":"https://openalex.org/I96908189","display_name":"Xinjiang University","ror":"https://ror.org/059gw8r13","country_code":"CN","type":"education","lineage":["https://openalex.org/I96908189"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"XINHUI AN","raw_affiliation_strings":["College of Mathematics and System Science, Xinjiang University, Urumqi, Xinjiang 830046, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and System Science, Xinjiang University, Urumqi, Xinjiang 830046, China","institution_ids":["https://openalex.org/I96908189"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3764,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.61562425,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"03","issue":"01","first_page":"17","last_page":"23"},"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/T11298","display_name":"Synthesis and Properties of Aromatic Compounds","score":0.9803000092506409,"subfield":{"id":"https://openalex.org/subfields/1605","display_name":"Organic Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9800999760627747,"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/wiener-index","display_name":"Wiener index","score":0.7975755929946899},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7888985872268677},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6853247880935669},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6132041811943054},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5084768533706665},{"id":"https://openalex.org/keywords/bound-graph","display_name":"Bound graph","score":0.462563157081604},{"id":"https://openalex.org/keywords/distance-regular-graph","display_name":"Distance-regular graph","score":0.46250078082084656},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.412627249956131},{"id":"https://openalex.org/keywords/cubic-graph","display_name":"Cubic graph","score":0.4100266098976135},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.40077272057533264},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.3447021245956421},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.21652573347091675}],"concepts":[{"id":"https://openalex.org/C16640446","wikidata":"https://www.wikidata.org/wiki/Q909065","display_name":"Wiener index","level":3,"score":0.7975755929946899},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7888985872268677},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6853247880935669},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6132041811943054},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5084768533706665},{"id":"https://openalex.org/C121134508","wikidata":"https://www.wikidata.org/wiki/Q4949882","display_name":"Bound graph","level":5,"score":0.462563157081604},{"id":"https://openalex.org/C56783289","wikidata":"https://www.wikidata.org/wiki/Q3115556","display_name":"Distance-regular graph","level":5,"score":0.46250078082084656},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.412627249956131},{"id":"https://openalex.org/C100500283","wikidata":"https://www.wikidata.org/wiki/Q1374495","display_name":"Cubic graph","level":5,"score":0.4100266098976135},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.40077272057533264},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.3447021245956421},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.21652573347091675}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830911000973","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830911000973","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":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.47999998927116394}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W74903757","https://openalex.org/W1484040084","https://openalex.org/W1971901968","https://openalex.org/W1980698230","https://openalex.org/W2021122901","https://openalex.org/W2029293322","https://openalex.org/W2068183381","https://openalex.org/W2076179359","https://openalex.org/W2078911265","https://openalex.org/W2137626924","https://openalex.org/W2154117231","https://openalex.org/W2318794083","https://openalex.org/W2319043422"],"related_works":["https://openalex.org/W2322051433","https://openalex.org/W4298388358","https://openalex.org/W2911324983","https://openalex.org/W2004791814","https://openalex.org/W2054731897","https://openalex.org/W2115626424","https://openalex.org/W2531609948","https://openalex.org/W3170778148","https://openalex.org/W2945649202","https://openalex.org/W2070569225"],"abstract_inverted_index":{"The":[0,41,85],"k":[1,11,28,82,95],"th":[2],"power":[3],"of":[4,45,78,91],"a":[5,14,46],"graph":[6,15,47,80,93],"G,":[7],"denoted":[8],"by":[9],"G":[10,27,36,48,57,81,94],",":[12],"is":[13,19,37,49,59,96],"whose":[16],"vertex":[17],"set":[18],"V(G),":[20],"two":[21],"distinct":[22],"vertices":[23,63],"being":[24],"adjacent":[25],"in":[26,35,67],"if":[29,32],"and":[30,65],"only":[31],"their":[33],"distance":[34,61],"at":[38],"most":[39],"k.":[40],"hyper-Wiener":[42,76],"index":[43,77],"WW(G)":[44],"defined":[50],"as":[51],"[Formula:":[52],"see":[53],"text],":[54],"where":[55],"d":[56],"(u,v)":[58],"the":[60,72,75,79,89,92],"between":[62],"u":[64],"v":[66],"G.":[68],"In":[69],"this":[70],"paper,":[71],"bounds":[73],"on":[74],"are":[83],"given.":[84],"Nordhaus\u2013Gaddum-type":[86],"inequality":[87],"for":[88],"hyper-Wiener-index":[90],"also":[97],"presented.":[98]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
