{"id":"https://openalex.org/W2989290433","doi":"https://doi.org/10.1109/access.2019.2953338","title":"Exact Formula and Improved Bounds for General Sum-Connectivity Index of Graph-Operations","display_name":"Exact Formula and Improved Bounds for General Sum-Connectivity Index of Graph-Operations","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2989290433","doi":"https://doi.org/10.1109/access.2019.2953338","mag":"2989290433"},"language":"en","primary_location":{"id":"doi:10.1109/access.2019.2953338","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2953338","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08897501.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08897501.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000900758","display_name":"Maqsood Ahmad","orcid":"https://orcid.org/0000-0002-6858-3244"},"institutions":[{"id":"https://openalex.org/I16076960","display_name":"COMSATS University Islamabad","ror":"https://ror.org/00nqqvk19","country_code":"PK","type":"education","lineage":["https://openalex.org/I16076960"]},{"id":"https://openalex.org/I87482320","display_name":"University of Management and Technology","ror":"https://ror.org/0095xcq10","country_code":"PK","type":"education","lineage":["https://openalex.org/I87482320"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Maqsood Ahmad","raw_affiliation_strings":["Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan","Department of Mathematics, School of Science, University of Management and Technology, Lahore, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan","institution_ids":["https://openalex.org/I16076960"]},{"raw_affiliation_string":"Department of Mathematics, School of Science, University of Management and Technology, Lahore, Pakistan","institution_ids":["https://openalex.org/I87482320"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001845294","display_name":"Muhammad Saeed","orcid":"https://orcid.org/0000-0002-7284-6908"},"institutions":[{"id":"https://openalex.org/I87482320","display_name":"University of Management and Technology","ror":"https://ror.org/0095xcq10","country_code":"PK","type":"education","lineage":["https://openalex.org/I87482320"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Saeed","raw_affiliation_strings":["Department of Mathematics, School of Science, University of Management and Technology, Lahore, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-7284-6908","affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Science, University of Management and Technology, Lahore, Pakistan","institution_ids":["https://openalex.org/I87482320"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037349396","display_name":"Muhammad Javaid","orcid":"https://orcid.org/0000-0001-7241-8172"},"institutions":[{"id":"https://openalex.org/I87482320","display_name":"University of Management and Technology","ror":"https://ror.org/0095xcq10","country_code":"PK","type":"education","lineage":["https://openalex.org/I87482320"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Javaid","raw_affiliation_strings":["Department of Mathematics, School of Science, University of Management and Technology, Lahore, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Science, University of Management and Technology, Lahore, Pakistan","institution_ids":["https://openalex.org/I87482320"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100727755","display_name":"Muhammad Tanveer Hussain","orcid":"https://orcid.org/0000-0003-0884-3056"},"institutions":[{"id":"https://openalex.org/I16076960","display_name":"COMSATS University Islamabad","ror":"https://ror.org/00nqqvk19","country_code":"PK","type":"education","lineage":["https://openalex.org/I16076960"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Hussain","raw_affiliation_strings":["Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan","institution_ids":["https://openalex.org/I16076960"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":5.6318,"has_fulltext":true,"cited_by_count":23,"citation_normalized_percentile":{"value":0.96949126,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"7","issue":null,"first_page":"167290","last_page":"167299"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9815000295639038,"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/T10083","display_name":"Graphene research and applications","score":0.9699000120162964,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5533638596534729},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5095620155334473},{"id":"https://openalex.org/keywords/index","display_name":"Index (typography)","score":0.4986448287963867},{"id":"https://openalex.org/keywords/graph-theory","display_name":"Graph theory","score":0.4443665146827698},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35366469621658325},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.2682439386844635},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.26296180486679077}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5533638596534729},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5095620155334473},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.4986448287963867},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.4443665146827698},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35366469621658325},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2682439386844635},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.26296180486679077},{"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:10.1109/access.2019.2953338","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2953338","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08897501.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:e38c35b0eccd4a49b6431fc5bed651d8","is_oa":true,"landing_page_url":"https://doaj.org/article/e38c35b0eccd4a49b6431fc5bed651d8","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":"IEEE Access, Vol 7, Pp 167290-167299 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2019.2953338","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2953338","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08897501.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2989290433.pdf","grobid_xml":"https://content.openalex.org/works/W2989290433.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W72434325","https://openalex.org/W623814603","https://openalex.org/W639608796","https://openalex.org/W1488799823","https://openalex.org/W1978629585","https://openalex.org/W1983169983","https://openalex.org/W1992105048","https://openalex.org/W1992611413","https://openalex.org/W1993943561","https://openalex.org/W2000076674","https://openalex.org/W2004163993","https://openalex.org/W2021229217","https://openalex.org/W2029713676","https://openalex.org/W2034405773","https://openalex.org/W2057073599","https://openalex.org/W2065534534","https://openalex.org/W2066891982","https://openalex.org/W2069528863","https://openalex.org/W2069962626","https://openalex.org/W2077669295","https://openalex.org/W2088365557","https://openalex.org/W2115325963","https://openalex.org/W2142066294","https://openalex.org/W2182995286","https://openalex.org/W2207432438","https://openalex.org/W2323784209","https://openalex.org/W2525866606","https://openalex.org/W2588026308","https://openalex.org/W2741270480","https://openalex.org/W2771900978","https://openalex.org/W2940495357","https://openalex.org/W4213151958","https://openalex.org/W6686009717","https://openalex.org/W6742063537"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644"],"abstract_inverted_index":{"For":[0],"a":[1],"molecular":[2,31],"graph":[3,32,54,74],"\u0393,":[4],"the":[5,23,26,30,65,101,105,126],"general":[6,69,106,142],"sum-connectivity":[7,70,107,143],"index":[8,47,71,108,144],"is":[9,48],"defined":[10],"as":[11],"\u03c7\u03b2(\u0393)":[12],"=\u03a3vw\u2208E(\u0393)[d\u0393(v)":[13],"+":[14],"d\u0393(w)]\u03b2,":[15],"where":[16,112],"\u03b2":[17,93],"\u2208":[18,94,114],"R":[19],"and":[20,41,57,81,99,124],"d\u0393(v)":[21],"denotes":[22],"degree":[24],"of":[25,36,49,68,104,128,141],"vertex":[27],"v":[28],"in":[29,52],"\u0393.":[33],"The":[34],"problem":[35],"finding":[37],"best":[38],"possible":[39],"upper":[40],"lower":[42],"bound":[43],"for":[44,72,92,109,145],"certain":[45],"topological":[46],"fundamental":[50],"nature":[51],"extremal":[53],"theory.":[55],"Akhtar":[56],"Imran":[58],"[J.":[59],"Inequal.":[60],"Appl.":[61,84],"(2016)":[62],"241]":[63],"obtained":[64,138],"sharp":[66,102,133],"bounds":[67,103,130],"four":[73],"operations":[75],"(F-sum":[76],"graphs)":[77],"introduced":[78],"by":[79],"Eliasi":[80],"Taeri":[82],"[Discrete":[83],"Math.":[85],"157:":[86],"794-803,":[87],"2009)].":[88],"In":[89,135],"this":[90],"paper,":[91],"N,":[95],"we":[96,137],"figured":[97],"out":[98],"improved":[100,129],"F-sum":[110,146],"graphs,":[111,147],"F":[113,149],"{R,":[115],"Q,":[116],"T}.":[117],"Several":[118],"examples":[119],"are":[120],"presented":[121],"to":[122],"elaborate":[123],"compare":[125],"results":[127],"with":[131],"existing":[132],"bounds.":[134],"addition,":[136],"exact":[139],"formula":[140],"when":[148],"=":[150],"S.":[151]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":6},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":6}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
