{"id":"https://openalex.org/W4399509027","doi":"https://doi.org/10.1142/s0129054124500060","title":"Limit Law for Zagreb and Wiener Indices of Random Exponential Recursive Trees","display_name":"Limit Law for Zagreb and Wiener Indices of Random Exponential Recursive Trees","publication_year":2024,"publication_date":"2024-06-08","ids":{"openalex":"https://openalex.org/W4399509027","doi":"https://doi.org/10.1142/s0129054124500060"},"language":"en","primary_location":{"id":"doi:10.1142/s0129054124500060","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054124500060","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"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":"International Journal of Foundations of Computer Science","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/A5108941624","display_name":"Ali Q. M. Al-Saedi","orcid":null},"institutions":[{"id":"https://openalex.org/I41832843","display_name":"University of Tabriz","ror":"https://ror.org/01papkj44","country_code":"IR","type":"education","lineage":["https://openalex.org/I41832843"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Ali Q. M. Al-Saedi","raw_affiliation_strings":["Department of Statistics, Faculty of Mathematical Sciences, University of Tabriz, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, Faculty of Mathematical Sciences, University of Tabriz, Iran","institution_ids":["https://openalex.org/I41832843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015751161","display_name":"Ramin Imany Nabiyyi","orcid":null},"institutions":[{"id":"https://openalex.org/I41832843","display_name":"University of Tabriz","ror":"https://ror.org/01papkj44","country_code":"IR","type":"education","lineage":["https://openalex.org/I41832843"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Ramin Imany Nabiyyi","raw_affiliation_strings":["Department of Statistics, Faculty of Mathematical Sciences, University of Tabriz, Iran"],"raw_orcid":"https://orcid.org/0000-0002-1981-2119","affiliations":[{"raw_affiliation_string":"Department of Statistics, Faculty of Mathematical Sciences, University of Tabriz, Iran","institution_ids":["https://openalex.org/I41832843"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018668884","display_name":"Mehri Javanian","orcid":"https://orcid.org/0000-0002-5737-3663"},"institutions":[{"id":"https://openalex.org/I99861883","display_name":"University of Zanjan","ror":"https://ror.org/05e34ej29","country_code":"IR","type":"education","lineage":["https://openalex.org/I99861883"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Mehri Javanian","raw_affiliation_strings":["Department of Statistics, Faculty of Sciences, University of Zanjan, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, Faculty of Sciences, University of Zanjan, Iran","institution_ids":["https://openalex.org/I99861883"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5108941624"],"corresponding_institution_ids":["https://openalex.org/I41832843"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14993519,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"36","issue":"01","first_page":"35","last_page":"48"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9814000129699707,"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":0.9814000129699707,"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/T13234","display_name":"advanced mathematical theories","score":0.9768999814987183,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.972100019454956,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7047702670097351},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6727469563484192},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5538182258605957},{"id":"https://openalex.org/keywords/limit-of-a-function","display_name":"Limit of a function","score":0.4303399920463562},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3990784287452698},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36837130784988403},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34846609830856323},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33301305770874023},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2690698802471161},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15051323175430298}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7047702670097351},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6727469563484192},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5538182258605957},{"id":"https://openalex.org/C19448537","wikidata":"https://www.wikidata.org/wiki/Q33540","display_name":"Limit of a function","level":3,"score":0.4303399920463562},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3990784287452698},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36837130784988403},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34846609830856323},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33301305770874023},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2690698802471161},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15051323175430298}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0129054124500060","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054124500060","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"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":"International Journal of Foundations of Computer Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7099999785423279,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1968569626","https://openalex.org/W1995153072","https://openalex.org/W2002494504","https://openalex.org/W2028039849","https://openalex.org/W2041147307","https://openalex.org/W2047055724","https://openalex.org/W2050682176","https://openalex.org/W2113913510","https://openalex.org/W2587761436","https://openalex.org/W2910294476","https://openalex.org/W3128161287","https://openalex.org/W4233699511"],"related_works":["https://openalex.org/W4224286489","https://openalex.org/W2361436100","https://openalex.org/W2348480070","https://openalex.org/W4385379825","https://openalex.org/W1564609195","https://openalex.org/W2390957572","https://openalex.org/W2381670468","https://openalex.org/W3000711322","https://openalex.org/W2367503346","https://openalex.org/W2355429547"],"abstract_inverted_index":{"The":[0],"Wiener":[1,47,104],"index":[2,19,81,105],"is":[3,20,107],"the":[4,17,23,28,41,46,69,74,85,92,110],"sum":[5,24],"of":[6,8,11,25,27,30,45,51,61,68,82,100,109,112],"distances":[7],"all":[9],"pairs":[10],"nodes":[12,31],"in":[13,32],"a":[14,33,78],"graph;":[15],"and":[16,48,96],"Zagreb":[18,49,80],"defined":[21],"as":[22],"squares":[26],"degrees":[29],"rooted":[34],"tree.":[35],"In":[36],"this":[37],"note,":[38],"we":[39,72,89],"calculate":[40],"first":[42],"two":[43,59,113],"moments":[44],"indices":[50],"random":[52],"exponential":[53],"recursive":[54],"trees":[55],"(random":[56],"ERTs)":[57],"from":[58],"systems":[60],"recurrence":[62],"relations.":[63],"Then,":[64],"by":[65],"an":[66,101],"application":[67],"contraction":[70],"method,":[71],"characterize":[73],"limit":[75],"law":[76],"for":[77],"scaled":[79,103],"ERTs.":[83],"Via":[84],"martingale":[86],"convergence":[87,95,99],"theorem,":[88],"also":[90],"show":[91],"almost":[93],"sure":[94],"quadratic":[97],"mean":[98],"appropriately":[102],"that":[106],"indicative":[108],"distance":[111],"randomly":[114],"chosen":[115],"nodes.":[116]},"counts_by_year":[],"updated_date":"2025-12-19T19:40:27.379048","created_date":"2025-10-10T00:00:00"}