{"id":"https://openalex.org/W2030654245","doi":"https://doi.org/10.1021/ci950116s","title":"Extensions of the Wiener Number","display_name":"Extensions of the Wiener Number","publication_year":1996,"publication_date":"1996-01-01","ids":{"openalex":"https://openalex.org/W2030654245","doi":"https://doi.org/10.1021/ci950116s","mag":"2030654245"},"language":"en","primary_location":{"id":"doi:10.1021/ci950116s","is_oa":false,"landing_page_url":"https://doi.org/10.1021/ci950116s","pdf_url":null,"source":{"id":"https://openalex.org/S171559003","display_name":"Journal of Chemical Information and Computer Sciences","issn_l":"0095-2338","issn":["0095-2338","1520-5142"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320006","host_organization_name":"American Chemical Society","host_organization_lineage":["https://openalex.org/P4310320006"],"host_organization_lineage_names":["American Chemical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Chemical Information and Computer Sciences","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/A5101572850","display_name":"Huijia Zhu","orcid":"https://orcid.org/0009-0008-5784-7225"},"institutions":[{"id":"https://openalex.org/I164185940","display_name":"Texas A&M University at Galveston","ror":"https://ror.org/00w0k4e67","country_code":"US","type":"education","lineage":["https://openalex.org/I164185940"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"H.-Y. Zhu","raw_affiliation_strings":["Texas A&M University at Galveston, Galveston, Texas 77553-1675, and Central Research Institute for Chemistry, Hungarian Academy of Science, H-1525 Budapest, P.O. Box 17, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Texas A&M University at Galveston, Galveston, Texas 77553-1675, and Central Research Institute for Chemistry, Hungarian Academy of Science, H-1525 Budapest, P.O. Box 17, Hungary","institution_ids":["https://openalex.org/I164185940"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065321757","display_name":"Douglas J. Klein","orcid":"https://orcid.org/0000-0002-5354-0065"},"institutions":[{"id":"https://openalex.org/I164185940","display_name":"Texas A&M University at Galveston","ror":"https://ror.org/00w0k4e67","country_code":"US","type":"education","lineage":["https://openalex.org/I164185940"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"D. J. Klein","raw_affiliation_strings":["Texas A&M University at Galveston, Galveston, Texas 77553-1675, and Central Research Institute for Chemistry, Hungarian Academy of Science, H-1525 Budapest, P.O. Box 17, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Texas A&M University at Galveston, Galveston, Texas 77553-1675, and Central Research Institute for Chemistry, Hungarian Academy of Science, H-1525 Budapest, P.O. Box 17, Hungary","institution_ids":["https://openalex.org/I164185940"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111544174","display_name":"I. Lukovits","orcid":null},"institutions":[{"id":"https://openalex.org/I164185940","display_name":"Texas A&M University at Galveston","ror":"https://ror.org/00w0k4e67","country_code":"US","type":"education","lineage":["https://openalex.org/I164185940"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"I. Lukovits","raw_affiliation_strings":["Texas A&M University at Galveston, Galveston, Texas 77553-1675, and Central Research Institute for Chemistry, Hungarian Academy of Science, H-1525 Budapest, P.O. Box 17, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Texas A&M University at Galveston, Galveston, Texas 77553-1675, and Central Research Institute for Chemistry, Hungarian Academy of Science, H-1525 Budapest, P.O. Box 17, Hungary","institution_ids":["https://openalex.org/I164185940"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I164185940"],"apc_list":null,"apc_paid":null,"fwci":3.2558,"has_fulltext":false,"cited_by_count":229,"citation_normalized_percentile":{"value":0.91974968,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"36","issue":"3","first_page":"420","last_page":"428"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9965999722480774,"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/T13297","display_name":"History and advancements in chemistry","score":0.9742000102996826,"subfield":{"id":"https://openalex.org/subfields/1606","display_name":"Physical and Theoretical 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/mathematics","display_name":"Mathematics","score":0.7193889617919922},{"id":"https://openalex.org/keywords/wiener-index","display_name":"Wiener index","score":0.6530221104621887},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5996057987213135},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5128102898597717},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4495656192302704},{"id":"https://openalex.org/keywords/vector-space","display_name":"Vector space","score":0.4416356086730957},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4000416696071625},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.39796584844589233},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.30652886629104614}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7193889617919922},{"id":"https://openalex.org/C16640446","wikidata":"https://www.wikidata.org/wiki/Q909065","display_name":"Wiener index","level":3,"score":0.6530221104621887},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5996057987213135},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5128102898597717},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4495656192302704},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.4416356086730957},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4000416696071625},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39796584844589233},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30652886629104614},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1021/ci950116s","is_oa":false,"landing_page_url":"https://doi.org/10.1021/ci950116s","pdf_url":null,"source":{"id":"https://openalex.org/S171559003","display_name":"Journal of Chemical Information and Computer Sciences","issn_l":"0095-2338","issn":["0095-2338","1520-5142"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320006","host_organization_name":"American Chemical Society","host_organization_lineage":["https://openalex.org/P4310320006"],"host_organization_lineage_names":["American Chemical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Chemical Information and Computer Sciences","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306196","display_name":"Welch Foundation","ror":"https://ror.org/00np6vq88"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W225487592","https://openalex.org/W306296506","https://openalex.org/W1963769212","https://openalex.org/W1966998243","https://openalex.org/W1973668233","https://openalex.org/W1974345530","https://openalex.org/W1983321303","https://openalex.org/W1984732727","https://openalex.org/W1994030344","https://openalex.org/W2007981503","https://openalex.org/W2011521683","https://openalex.org/W2029236883","https://openalex.org/W2040494696","https://openalex.org/W2071128523","https://openalex.org/W2085908220","https://openalex.org/W2090037068","https://openalex.org/W2118237959","https://openalex.org/W2154117231","https://openalex.org/W2409065277","https://openalex.org/W2773462233","https://openalex.org/W4247782380","https://openalex.org/W4252247665"],"related_works":["https://openalex.org/W2078745726","https://openalex.org/W2752599497","https://openalex.org/W1964911879","https://openalex.org/W2382103610","https://openalex.org/W2184335448","https://openalex.org/W2361011542","https://openalex.org/W2949527626","https://openalex.org/W2384431448","https://openalex.org/W3189256254","https://openalex.org/W4214536291"],"abstract_inverted_index":{"Particularly":[0],"for":[1,53,114,117,126,161],"structure\u2212property":[2],"correlations":[3],"there":[4,73],"are":[5,39,74,100,187],"many":[6],"chemical":[7],"graph-theoretic":[8],"indices,":[9],"one":[10,25,83],"of":[11,30,37,43,78,84,91,129,137,147,158,171,177,185,209,212],"which":[12,38,162],"is":[13,70,121,124,149,166],"Wiener's":[14,18],"\u201cpath":[15],"number\u201d.":[16],"Because":[17],"original":[19],"work":[20],"focused":[21],"on":[22],"acyclic":[23],"structures,":[24,35],"can":[26,202],"imagine":[27],"different":[28,45,59,119,183],"ways":[29],"extending":[31],"it":[32,69],"to":[33,63,82,89,104,134,142,150,180,189],"cycle-containing":[34],"several":[36],"noted":[40,188],"here.":[41],"Many":[42],"these":[44],"formulas":[46,60,79],"in":[47,132,196,207],"fact":[48],"yield":[49],"like":[50],"numerical":[51],"values":[52],"general":[54],"connected":[55],"graphs":[56],"that":[57,72,199],"is,":[58],"sometimes":[61],"correspond":[62],"the":[64,94,97,143,163,167,197,210,213],"same":[65],"graph":[66,139,159],"invariant.":[67],"Indeed":[68],"found":[71,103],"two":[75,85],"\u201cdominant\u201d":[76],"classes":[77],"each":[80],"corresponding":[81],"distinct":[86,106],"invariants.":[87],"Extensions":[88],"sequences":[90,120,131],"invariants":[92,160,178],"(with":[93],"Wiener":[95,164],"index":[96,165],"first":[98,169],"member)":[99],"more":[101],"often":[102],"give":[105],"sequences.":[107],"Further":[108],"a":[109,127,135,152,194],"powerful":[110],"vector-space":[111],"theoretic":[112],"view":[113],"characterizing":[115],"and":[116],"comparing":[118],"described.":[122],"This":[123],"illustrated":[125],"collection":[128],"eight":[130],"application":[133],"set":[136,157],"molecular":[138],"structures":[140],"(corresponding":[141,179],"octanes).":[144],"Another":[145],"type":[146],"extension":[148],"generate":[151],"sequence":[153],"or":[154],"partially":[155],"ordered":[156],"natural":[168],"member":[170],"this":[172],"set.":[173,214],"Certain":[174],"such":[175],"sets":[176],"contributions":[181],"from":[182],"types":[184],"subgraphs)":[186],"be":[190,203],"\u201ccomplete\u201d":[191],"(or":[192],"form":[193],"basis)":[195],"sense":[198],"any":[200],"invariant":[201],"faithfully":[204],"linearly":[205],"expanded":[206],"terms":[208],"members":[211]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":16},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":14},{"year":2020,"cited_by_count":20},{"year":2019,"cited_by_count":19},{"year":2018,"cited_by_count":17},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":11},{"year":2014,"cited_by_count":13},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":7}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}