{"id":"https://openalex.org/W4308196335","doi":"https://doi.org/10.1080/09728600.2022.2140088","title":"Wiener index of graphs over rings: a survey","display_name":"Wiener index of graphs over rings: a survey","publication_year":2022,"publication_date":"2022-09-02","ids":{"openalex":"https://openalex.org/W4308196335","doi":"https://doi.org/10.1080/09728600.2022.2140088"},"language":"en","primary_location":{"id":"doi:10.1080/09728600.2022.2140088","is_oa":true,"landing_page_url":"https://doi.org/10.1080/09728600.2022.2140088","pdf_url":null,"source":{"id":"https://openalex.org/S2764899362","display_name":"AKCE International Journal of Graphs and Combinatorics","issn_l":"0972-8600","issn":["0972-8600","2543-3474"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AKCE International Journal of Graphs and Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1080/09728600.2022.2140088","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043549643","display_name":"T. Asir","orcid":"https://orcid.org/0000-0002-9035-6996"},"institutions":[{"id":"https://openalex.org/I175691731","display_name":"Pondicherry University","ror":"https://ror.org/01a3mef16","country_code":"IN","type":"education","lineage":["https://openalex.org/I175691731"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"T. Asir","raw_affiliation_strings":["Department of Mathematics, Pondicherry University, Puducherry, India"],"raw_orcid":"https://orcid.org/0000-0002-9035-6996","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Pondicherry University, Puducherry, India","institution_ids":["https://openalex.org/I175691731"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078554704","display_name":"V. Rabikka","orcid":null},"institutions":[{"id":"https://openalex.org/I13268429","display_name":"Madurai Kamaraj University","ror":"https://ror.org/04c8e9019","country_code":"IN","type":"education","lineage":["https://openalex.org/I13268429"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"V. Rabikka","raw_affiliation_strings":["Department of Mathematics-DDE, Madurai Kamaraj University, Madurai, Tamil Nadu, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics-DDE, Madurai Kamaraj University, Madurai, Tamil Nadu, India","institution_ids":["https://openalex.org/I13268429"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004602920","display_name":"A. M. Anto","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. M. Anto","raw_affiliation_strings":["Department of Mathematics, St. Albert\u2019s College, Kochi, Kerala, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, St. Albert\u2019s College, Kochi, Kerala, India","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067214476","display_name":"N. Shunmugapriya","orcid":null},"institutions":[{"id":"https://openalex.org/I4399598407","display_name":"G. Venkataswamy Naidu College","ror":"https://ror.org/02ddybj40","country_code":null,"type":"education","lineage":["https://openalex.org/I4399598407"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"N. Shunmugapriya","raw_affiliation_strings":["Department of Mathematics, G. Venkataswamy Naidu College, Kovilpatti, Tamil Nadu, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, G. Venkataswamy Naidu College, Kovilpatti, Tamil Nadu, India","institution_ids":["https://openalex.org/I4399598407"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5043549643"],"corresponding_institution_ids":["https://openalex.org/I175691731"],"apc_list":{"value":1000,"currency":"GBP","value_usd":1226},"apc_paid":{"value":1000,"currency":"GBP","value_usd":1226},"fwci":4.8116,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.964672,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"19","issue":"3","first_page":"316","last_page":"324"},"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/T10849","display_name":"Finite Group Theory Research","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.9915000200271606,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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":0.8248457312583923},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6449443101882935},{"id":"https://openalex.org/keywords/wiener-index","display_name":"Wiener index","score":0.5076431035995483},{"id":"https://openalex.org/keywords/indifference-graph","display_name":"Indifference graph","score":0.5073265433311462},{"id":"https://openalex.org/keywords/index","display_name":"Index (typography)","score":0.46044835448265076},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.4579554796218872},{"id":"https://openalex.org/keywords/cograph","display_name":"Cograph","score":0.4453832507133484},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38904115557670593},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.37160730361938477},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.2125183641910553},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09198477864265442}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8248457312583923},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6449443101882935},{"id":"https://openalex.org/C16640446","wikidata":"https://www.wikidata.org/wiki/Q909065","display_name":"Wiener index","level":3,"score":0.5076431035995483},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.5073265433311462},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.46044835448265076},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.4579554796218872},{"id":"https://openalex.org/C59824394","wikidata":"https://www.wikidata.org/wiki/Q5141281","display_name":"Cograph","level":5,"score":0.4453832507133484},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38904115557670593},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.37160730361938477},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.2125183641910553},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09198477864265442},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/09728600.2022.2140088","is_oa":true,"landing_page_url":"https://doi.org/10.1080/09728600.2022.2140088","pdf_url":null,"source":{"id":"https://openalex.org/S2764899362","display_name":"AKCE International Journal of Graphs and Combinatorics","issn_l":"0972-8600","issn":["0972-8600","2543-3474"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AKCE International Journal of Graphs and Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:1f91a8d27265441abbce04be976e5c12","is_oa":true,"landing_page_url":"https://doaj.org/article/1f91a8d27265441abbce04be976e5c12","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"AKCE International Journal of Graphs and Combinatorics, Vol 19, Iss 3, Pp 316-324 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1080/09728600.2022.2140088","is_oa":true,"landing_page_url":"https://doi.org/10.1080/09728600.2022.2140088","pdf_url":null,"source":{"id":"https://openalex.org/S2764899362","display_name":"AKCE International Journal of Graphs and Combinatorics","issn_l":"0972-8600","issn":["0972-8600","2543-3474"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AKCE International Journal of Graphs and Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W74903757","https://openalex.org/W1964613552","https://openalex.org/W1971564848","https://openalex.org/W1972658342","https://openalex.org/W1973293130","https://openalex.org/W1980698230","https://openalex.org/W1987023204","https://openalex.org/W1999818549","https://openalex.org/W2000462523","https://openalex.org/W2002257546","https://openalex.org/W2018756269","https://openalex.org/W2029302951","https://openalex.org/W2039024143","https://openalex.org/W2042734910","https://openalex.org/W2044882319","https://openalex.org/W2085223600","https://openalex.org/W2123034613","https://openalex.org/W2154117231","https://openalex.org/W2318794083","https://openalex.org/W2773640017","https://openalex.org/W2959544132","https://openalex.org/W2963176950","https://openalex.org/W2998663017","https://openalex.org/W3136378898","https://openalex.org/W3209391632","https://openalex.org/W4210908572","https://openalex.org/W4225426947"],"related_works":["https://openalex.org/W4220852510","https://openalex.org/W4385327816","https://openalex.org/W4385588236","https://openalex.org/W3139101777","https://openalex.org/W2949743119","https://openalex.org/W1811797198","https://openalex.org/W2041783376","https://openalex.org/W2083238533","https://openalex.org/W603403972","https://openalex.org/W2061237693"],"abstract_inverted_index":{"AbstractThis":[0],"article":[1],"presents":[2],"a":[3],"survey":[4],"of":[5,8,12],"results":[6],"consisting":[7],"the":[9,41],"Wiener":[10],"index":[11],"graphs":[13,28,42],"associated":[14],"with":[15],"commutative":[16],"rings.":[17],"In":[18],"particular,":[19],"we":[20,33],"focus":[21],"on":[22],"zero-divisor":[23],"graphs,":[24,26],"unit":[25],"total":[27],"and":[29],"prime":[30],"graphs.":[31],"Further,":[32],"have":[34],"posed":[35],"some":[36],"open":[37],"problems":[38],"corresponding":[39],"to":[40],"considered.":[43]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":6}],"updated_date":"2026-05-20T08:49:12.498775","created_date":"2025-10-10T00:00:00"}
