{"id":"https://openalex.org/W4411744695","doi":"https://doi.org/10.1007/s40314-025-03296-7","title":"On the Wiener-like root-indices of graphs","display_name":"On the Wiener-like root-indices of graphs","publication_year":2025,"publication_date":"2025-06-28","ids":{"openalex":"https://openalex.org/W4411744695","doi":"https://doi.org/10.1007/s40314-025-03296-7"},"language":"en","primary_location":{"id":"doi:10.1007/s40314-025-03296-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40314-025-03296-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40314-025-03296-7.pdf","source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"0101-8205","issn":["0101-8205","1807-0302","2238-3603"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s40314-025-03296-7.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079920794","display_name":"Simon Brezovnik","orcid":"https://orcid.org/0000-0001-6584-6435"},"institutions":[{"id":"https://openalex.org/I153976015","display_name":"University of Ljubljana","ror":"https://ror.org/05njb9z20","country_code":"SI","type":"education","lineage":["https://openalex.org/I153976015"]},{"id":"https://openalex.org/I4210106342","display_name":"Institute of Mathematics, Physics, and Mechanics","ror":"https://ror.org/01eb3qa50","country_code":"SI","type":"facility","lineage":["https://openalex.org/I4210106342"]}],"countries":["SI"],"is_corresponding":false,"raw_author_name":"Simon Brezovnik","raw_affiliation_strings":["Faculty of Mechanical Engineering, University of Ljubljana, Ljubljana, Slovenia","Institute of Mathematics, Physics, and Mechanics, Ljubljana, Slovenia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mechanical Engineering, University of Ljubljana, Ljubljana, Slovenia","institution_ids":["https://openalex.org/I153976015"]},{"raw_affiliation_string":"Institute of Mathematics, Physics, and Mechanics, Ljubljana, Slovenia","institution_ids":["https://openalex.org/I4210106342"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044244385","display_name":"Matthias Dehmer","orcid":"https://orcid.org/0000-0001-8454-5857"},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]},{"id":"https://openalex.org/I4210110558","display_name":"Xi'an Technological University","ror":"https://ror.org/01t8prc81","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210110558"]},{"id":"https://openalex.org/I4210114246","display_name":"UMIT - Private Universit\u00e4t f\u00fcr Gesundheitswissenschaften, Medizinische Informatik und Technik","ror":"https://ror.org/02d0kps43","country_code":"AT","type":"education","lineage":["https://openalex.org/I4210114246"]},{"id":"https://openalex.org/I4210116528","display_name":"Swiss Distance University of Applied Sciences","ror":"https://ror.org/01t75ff47","country_code":"CH","type":"education","lineage":["https://openalex.org/I4210116528"]}],"countries":["AT","CH","CN"],"is_corresponding":false,"raw_author_name":"Matthias Dehmer","raw_affiliation_strings":["College of Artificial Intelligence, Nankai University, Tianjin, China","Department for Biomedical Computer Science and Mechatronics, UMIT-Private University for Health Sciences, Medical Informatics and Technology, Hall in Tyrol, Austria","School of Science, Xi\u2019an Technological University, Xi\u2019an, Shaanxi, China","Swiss Distance University of Applied Sciences, Brig, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Artificial Intelligence, Nankai University, Tianjin, China","institution_ids":["https://openalex.org/I205237279"]},{"raw_affiliation_string":"Department for Biomedical Computer Science and Mechatronics, UMIT-Private University for Health Sciences, Medical Informatics and Technology, Hall in Tyrol, Austria","institution_ids":["https://openalex.org/I4210114246"]},{"raw_affiliation_string":"School of Science, Xi\u2019an Technological University, Xi\u2019an, Shaanxi, China","institution_ids":["https://openalex.org/I4210110558"]},{"raw_affiliation_string":"Swiss Distance University of Applied Sciences, Brig, Switzerland","institution_ids":["https://openalex.org/I4210116528"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075284723","display_name":"Niko Tratnik","orcid":"https://orcid.org/0000-0002-5564-049X"},"institutions":[{"id":"https://openalex.org/I37696226","display_name":"University of Maribor","ror":"https://ror.org/01d5jce07","country_code":"SI","type":"education","lineage":["https://openalex.org/I37696226"]},{"id":"https://openalex.org/I4210106342","display_name":"Institute of Mathematics, Physics, and Mechanics","ror":"https://ror.org/01eb3qa50","country_code":"SI","type":"facility","lineage":["https://openalex.org/I4210106342"]}],"countries":["SI"],"is_corresponding":true,"raw_author_name":"Niko Tratnik","raw_affiliation_strings":["Faculty of Natural Sciences and Mathematics, University of Maribor, Maribor, Slovenia","Institute of Mathematics, Physics, and Mechanics, Ljubljana, Slovenia"],"raw_orcid":"https://orcid.org/0000-0002-5564-049X","affiliations":[{"raw_affiliation_string":"Faculty of Natural Sciences and Mathematics, University of Maribor, Maribor, Slovenia","institution_ids":["https://openalex.org/I37696226"]},{"raw_affiliation_string":"Institute of Mathematics, Physics, and Mechanics, Ljubljana, Slovenia","institution_ids":["https://openalex.org/I4210106342"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077878330","display_name":"Petra \u017digert Pleter\u0161ek","orcid":null},"institutions":[{"id":"https://openalex.org/I37696226","display_name":"University of Maribor","ror":"https://ror.org/01d5jce07","country_code":"SI","type":"education","lineage":["https://openalex.org/I37696226"]}],"countries":["SI"],"is_corresponding":false,"raw_author_name":"Petra \u017digert Pleter\u0161ek","raw_affiliation_strings":["Faculty of Chemistry and Chemical Engineering, University of Maribor, Maribor, Slovenia","Faculty of Natural Sciences and Mathematics, University of Maribor, Maribor, Slovenia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Chemistry and Chemical Engineering, University of Maribor, Maribor, Slovenia","institution_ids":["https://openalex.org/I37696226"]},{"raw_affiliation_string":"Faculty of Natural Sciences and Mathematics, University of Maribor, Maribor, Slovenia","institution_ids":["https://openalex.org/I37696226"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5075284723"],"corresponding_institution_ids":["https://openalex.org/I37696226","https://openalex.org/I4210106342"],"apc_list":null,"apc_paid":null,"fwci":2.6684,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.86948164,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":97},"biblio":{"volume":"44","issue":"7","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9990000128746033,"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":0.9990000128746033,"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/T13297","display_name":"History and advancements in chemistry","score":0.988099992275238,"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"}},{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9801999926567078,"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/root","display_name":"Root (linguistics)","score":0.7187981605529785},{"id":"https://openalex.org/keywords/wiener-index","display_name":"Wiener index","score":0.7000402212142944},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5623201131820679},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3486735224723816},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2693413496017456},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.17543044686317444},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.15372249484062195},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.13431349396705627}],"concepts":[{"id":"https://openalex.org/C171078966","wikidata":"https://www.wikidata.org/wiki/Q111029","display_name":"Root (linguistics)","level":2,"score":0.7187981605529785},{"id":"https://openalex.org/C16640446","wikidata":"https://www.wikidata.org/wiki/Q909065","display_name":"Wiener index","level":3,"score":0.7000402212142944},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5623201131820679},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3486735224723816},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2693413496017456},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.17543044686317444},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.15372249484062195},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.13431349396705627}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s40314-025-03296-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40314-025-03296-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40314-025-03296-7.pdf","source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"0101-8205","issn":["0101-8205","1807-0302","2238-3603"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s40314-025-03296-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40314-025-03296-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40314-025-03296-7.pdf","source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"0101-8205","issn":["0101-8205","1807-0302","2238-3603"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1053787376","display_name":null,"funder_award_id":"L7-4494","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"},{"id":"https://openalex.org/G3894112125","display_name":null,"funder_award_id":"P1-0297","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"},{"id":"https://openalex.org/G4439903903","display_name":null,"funder_award_id":"N1-0278","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"},{"id":"https://openalex.org/G5957385805","display_name":null,"funder_award_id":"N1-0285","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"},{"id":"https://openalex.org/G8810894625","display_name":null,"funder_award_id":"J1-4031","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"}],"funders":[{"id":"https://openalex.org/F4320322554","display_name":"Javna Agencija za Raziskovalno Dejavnost RS","ror":"https://ror.org/059bp8k51"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4411744695.pdf","grobid_xml":"https://content.openalex.org/works/W4411744695.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W623814603","https://openalex.org/W1520184440","https://openalex.org/W1545231783","https://openalex.org/W1974698748","https://openalex.org/W1983681808","https://openalex.org/W1989042465","https://openalex.org/W2007981503","https://openalex.org/W2010541316","https://openalex.org/W2012513251","https://openalex.org/W2028286289","https://openalex.org/W2028386337","https://openalex.org/W2031217417","https://openalex.org/W2032040845","https://openalex.org/W2058423036","https://openalex.org/W2060907307","https://openalex.org/W2065534534","https://openalex.org/W2086920981","https://openalex.org/W2143401511","https://openalex.org/W2318794083","https://openalex.org/W2948360268","https://openalex.org/W3004280721","https://openalex.org/W3153357212","https://openalex.org/W3159466399","https://openalex.org/W3199375174","https://openalex.org/W4382402164","https://openalex.org/W4405184155"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2078745726","https://openalex.org/W4395018287","https://openalex.org/W4392824932","https://openalex.org/W2752599497","https://openalex.org/W1964911879","https://openalex.org/W1979597421","https://openalex.org/W2119196129","https://openalex.org/W1569179256","https://openalex.org/W2382103610"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper,":[3],"we":[4,22,41,106],"examine":[5],"roots":[6,12,28,74,133],"of":[7,29,58,75,86,97,111,123,134,149,168],"graph":[8,18,32,60,124,135],"polynomials":[9,33,66,136],"where":[10],"those":[11,112],"can":[13,90],"be":[14,91],"considered":[15],"as":[16,70,115],"structural":[17],"measures.":[19,125],"More":[20],"precisely,":[21],"prove":[23],"analytical":[24,100],"results":[25,89,101],"for":[26,93],"the":[27,44,46,49,73,84,94,130],"certain":[30],"modified":[31,77],"and":[34,48,72,104,171],"also":[35,107],"discuss":[36],"numerical":[37],"results.":[38],"As":[39],"polynomials,":[40],"use,":[42],"e.g.,":[43],"Hosoya,":[45],"Schultz,":[47],"Gutman":[50],"polynomial":[51],"which":[52,118,145],"belong":[53],"to":[54,82,161],"an":[55,120],"interesting":[56],"family":[57],"degree-distance-based":[59],"polynomials;":[61],"they":[62],"constitute":[63],"so-called":[64],"counting":[65],"with":[67],"non-negative":[68],"integers":[69],"coefficients":[71],"their":[76,116],"versions":[78,148],"have":[79],"been":[80],"used":[81],"characterize":[83],"topology":[85],"graphs.":[87,98],"Our":[88],"applied":[92],"quantitative":[95],"characterization":[96],"Besides":[99],"on":[102,141],"bounds":[103],"convergence,":[105],"investigate":[108],"other":[109],"properties":[110],"measures":[113,131],"such":[114],"degeneracy":[117],"is":[119,156],"undesired":[121],"aspect":[122],"It":[126],"turns":[127],"out":[128],"that":[129,158],"representing":[132],"possess":[137],"high":[138],"discrimination":[139],"power":[140],"exhaustively":[142],"generated":[143],"trees,":[144],"outperforms":[146],"standard":[147],"these":[150],"indices.":[151],"Furthermore,":[152],"a":[153],"new":[154],"measure":[155],"introduced":[157],"allows":[159],"us":[160],"compare":[162],"different":[163],"topological":[164],"indices":[165],"in":[166],"terms":[167],"structure":[169],"sensitivity":[170],"abruptness.":[172]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-07-07T14:30:12.667765","created_date":"2025-10-10T00:00:00"}