{"id":"https://openalex.org/W3208149899","doi":"https://doi.org/10.1155/2021/6616056","title":"Properties of Total Transformation Graphs for General Sum\u2010Connectivity Index","display_name":"Properties of Total Transformation Graphs for General Sum\u2010Connectivity Index","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3208149899","doi":"https://doi.org/10.1155/2021/6616056","mag":"3208149899"},"language":"en","primary_location":{"id":"doi:10.1155/2021/6616056","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2021/6616056","pdf_url":"https://downloads.hindawi.com/journals/complexity/2021/6616056.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/complexity/2021/6616056.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102812314","display_name":"Anam Rani","orcid":"https://orcid.org/0000-0003-3505-6074"},"institutions":[{"id":"https://openalex.org/I4626487","display_name":"King Faisal University","ror":"https://ror.org/00dn43547","country_code":"SA","type":"education","lineage":["https://openalex.org/I4626487"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Anam Rani","raw_affiliation_strings":["Department of Basic Sciences, Deanship of Preparatory Year, King Faisal University Al Ahsa, Al Hofuf,  Saudi Arabia","King Faisal University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Basic Sciences, Deanship of Preparatory Year, King Faisal University Al Ahsa, Al Hofuf,  Saudi Arabia","institution_ids":["https://openalex.org/I4626487"]},{"raw_affiliation_string":"King Faisal University","institution_ids":["https://openalex.org/I4626487"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024364073","display_name":"Muhammad Imran","orcid":"https://orcid.org/0000-0002-2827-0462"},"institutions":[{"id":"https://openalex.org/I201726411","display_name":"United Arab Emirates University","ror":"https://ror.org/01km6p862","country_code":"AE","type":"education","lineage":["https://openalex.org/I201726411"]}],"countries":["AE"],"is_corresponding":true,"raw_author_name":"Muhammad Imran","raw_affiliation_strings":["Department of Mathematical Sciences, United Arab Emirates University, P.O. Box 15551, Al Ain,  UAE uaeu.ac.ae","United Arab Emirates University"],"raw_orcid":"https://orcid.org/0000-0002-2827-0462","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, United Arab Emirates University, P.O. Box 15551, Al Ain,  UAE uaeu.ac.ae","institution_ids":["https://openalex.org/I201726411"]},{"raw_affiliation_string":"United Arab Emirates University","institution_ids":["https://openalex.org/I201726411"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055955473","display_name":"Asima Razzaque","orcid":"https://orcid.org/0000-0002-7579-8972"},"institutions":[{"id":"https://openalex.org/I4626487","display_name":"King Faisal University","ror":"https://ror.org/00dn43547","country_code":"SA","type":"education","lineage":["https://openalex.org/I4626487"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Asima Razzaque","raw_affiliation_strings":["Department of Basic Sciences, Deanship of Preparatory Year, King Faisal University Al Ahsa, Al Hofuf,  Saudi Arabia","King Faisal University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Basic Sciences, Deanship of Preparatory Year, King Faisal University Al Ahsa, Al Hofuf,  Saudi Arabia","institution_ids":["https://openalex.org/I4626487"]},{"raw_affiliation_string":"King Faisal University","institution_ids":["https://openalex.org/I4626487"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038230048","display_name":"Usman Ali","orcid":"https://orcid.org/0000-0003-0084-5954"},"institutions":[{"id":"https://openalex.org/I127670440","display_name":"Bahauddin Zakariya University","ror":"https://ror.org/05x817c41","country_code":"PK","type":"education","lineage":["https://openalex.org/I127670440"]},{"id":"https://openalex.org/I3017942884","display_name":"Institut de Math\u00e9matiques de Jussieu-Paris Rive Gauche","ror":"https://ror.org/03fk87k11","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I3017942884","https://openalex.org/I39804081","https://openalex.org/I4210141950"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]}],"countries":["FR","PK"],"is_corresponding":false,"raw_author_name":"Usman Ali","raw_affiliation_strings":["CASPAM, Bahauddin Zakariya University, Multan 66000,  Pakistan bzu.edu.pk","Institute de Mathematiques de Jussieu-Paris Rive Gauche-Paris, France (Universite de Paris/Sorbonne Universite), Paris,  France","Bahauddin Zakariya University","Institut de Math\u00e9matiques de Jussieu - Paris Rive Gauche"],"raw_orcid":"https://orcid.org/0000-0003-0084-5954","affiliations":[{"raw_affiliation_string":"CASPAM, Bahauddin Zakariya University, Multan 66000,  Pakistan bzu.edu.pk","institution_ids":["https://openalex.org/I127670440"]},{"raw_affiliation_string":"Institute de Mathematiques de Jussieu-Paris Rive Gauche-Paris, France (Universite de Paris/Sorbonne Universite), Paris,  France","institution_ids":["https://openalex.org/I3017942884","https://openalex.org/I39804081"]},{"raw_affiliation_string":"Bahauddin Zakariya University","institution_ids":["https://openalex.org/I127670440"]},{"raw_affiliation_string":"Institut de Math\u00e9matiques de Jussieu - Paris Rive Gauche","institution_ids":["https://openalex.org/I3017942884"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5024364073"],"corresponding_institution_ids":["https://openalex.org/I201726411"],"apc_list":{"value":2550,"currency":"USD","value_usd":2550},"apc_paid":{"value":2550,"currency":"USD","value_usd":2550},"fwci":0.4029,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.62365217,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"2021","issue":"1","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":0.9998000264167786,"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":0.9973999857902527,"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.9778000116348267,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/index","display_name":"Index (typography)","score":0.43326103687286377},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.43093088269233704},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41760730743408203},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3437357544898987},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33870935440063477},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30532604455947876},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.10627785325050354}],"concepts":[{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.43326103687286377},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.43093088269233704},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41760730743408203},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3437357544898987},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33870935440063477},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30532604455947876},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.10627785325050354}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2021/6616056","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2021/6616056","pdf_url":"https://downloads.hindawi.com/journals/complexity/2021/6616056.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-03430901v1","is_oa":true,"landing_page_url":"https://hal.sorbonne-universite.fr/hal-03430901","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complexity, 2021, 2021, pp.1 - 6. ⟨10.1155/2021/6616056⟩","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:RePEc:hin:complx:6616056","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/complexity/2021/6616056.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:d5cea30b33f14ea7a903b07b7647c3a2","is_oa":true,"landing_page_url":"https://doaj.org/article/d5cea30b33f14ea7a903b07b7647c3a2","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":"Complexity, Vol 2021 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2021/6616056","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2021/6616056","pdf_url":"https://downloads.hindawi.com/journals/complexity/2021/6616056.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9","score":0.5799999833106995}],"awards":[{"id":"https://openalex.org/G2099851399","display_name":null,"funder_award_id":"G00003271","funder_id":"https://openalex.org/F4320323593","funder_display_name":"United Arab Emirates University"},{"id":"https://openalex.org/G2216294503","display_name":null,"funder_award_id":"G00003461","funder_id":"https://openalex.org/F4320323593","funder_display_name":"United Arab Emirates University"}],"funders":[{"id":"https://openalex.org/F4320322804","display_name":"Deanship of Scientific Research, King Faisal University","ror":"https://ror.org/00dn43547"},{"id":"https://openalex.org/F4320323593","display_name":"United Arab Emirates University","ror":"https://ror.org/01km6p862"},{"id":"https://openalex.org/F4320331156","display_name":"King Faisal University","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3208149899.pdf","grobid_xml":"https://content.openalex.org/works/W3208149899.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1983169983","https://openalex.org/W1991520783","https://openalex.org/W1993943561","https://openalex.org/W1995280763","https://openalex.org/W2018708200","https://openalex.org/W2021229217","https://openalex.org/W2034405773","https://openalex.org/W2057073599","https://openalex.org/W2066891982","https://openalex.org/W2069962626","https://openalex.org/W2077669295","https://openalex.org/W2113091544","https://openalex.org/W2115325963","https://openalex.org/W2187414734","https://openalex.org/W2297067969","https://openalex.org/W2512269750","https://openalex.org/W2525866606","https://openalex.org/W2552116743","https://openalex.org/W2559947018","https://openalex.org/W2606545786","https://openalex.org/W2741527348","https://openalex.org/W2772519158","https://openalex.org/W2891747133","https://openalex.org/W2952091746","https://openalex.org/W2955041009","https://openalex.org/W2978010002","https://openalex.org/W4240502307","https://openalex.org/W6742277795"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2042127053","https://openalex.org/W2142036596","https://openalex.org/W2072657027"],"abstract_inverted_index":{"The":[0,91,116],"study":[1,149],"of":[2,13,19,35,46,60,80,85,89,96,106,154,160],"networks":[3],"and":[4,49,75,110,127,134],"graphs":[5,51,156],"through":[6],"structural":[7,25,33],"properties":[8,26],"is":[9,27,83,98,112,119,125],"a":[10,69,113,120],"massive":[11],"area":[12],"research":[14],"with":[15],"developing":[16],"significance.":[17],"One":[18],"the":[20,36,40,57,78,86,104,107,150],"methods":[21],"used":[22,54],"in":[23,72,109,132,143],"studying":[24],"obtaining":[28],"quantitative":[29],"measures":[30],"that":[31],"encode":[32],"data":[34],"whole":[37,58],"network":[38],"by":[39,162],"real":[41,114],"number.":[42,115],"A":[43],"large":[44],"collection":[45],"numerical":[47],"descriptors":[48],"associated":[50],"have":[52,68],"been":[53],"to":[55],"examine":[56],"structure":[59],"networks.":[61],"In":[62,145],"these":[63],"analyses,":[64],"degree\u2010related":[65,81],"topological":[66],"indices":[67,82],"significant":[70],"position":[71],"theoretical":[73],"chemistry":[74],"nanotechnology.":[76],"Thus,":[77],"computation":[79],"one":[84],"successful":[87],"topics":[88],"research.":[90],"general":[92,151],"sum\u2010connectivity":[93,152],"(GSC)":[94],"index":[95,153],"graph":[97,118,121],"described":[99],"as":[100],",":[101,126],"where":[102],"presents":[103],"degree":[105],"vertex":[108,123],"\u03c1":[111,161],"total":[117,155],"whose":[122],"set":[124],"two":[128],"vertices":[129],"are":[130,138],"linked":[131],"if":[133,136],"only":[135],"they":[137],"either":[139],"adjacent":[140],"or":[141],"incident":[142],".":[144],"this":[146],"article,":[147],"we":[148],"for":[157],"different":[158],"values":[159],"using":[163],"Jensen\u2019s":[164],"inequality.":[165]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}