{"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":4,"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":6.0779,"has_fulltext":true,"cited_by_count":23,"citation_normalized_percentile":{"value":0.97201726,"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":{"pdf":true,"grobid_xml":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":[2,58],"graph":[3,59,81,101],"\u0393,":[4],"the":[5,50,53,57,92,128,132,153],"general":[6,96,133,169],"sum-connectivity":[7,97,134,170],"index":[8,74,98,135,171],"is":[9,75],"defined":[10],"as":[11],"\u03c7":[12],"<sub":[13,21,25,31,45],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[14,19,22,26,32,36,46],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u03b2</sub>":[15],"(\u0393)":[16],"=":[17,177],"<b":[18],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u03a3</b>":[20],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">vw\u2208E(\u0393)</sub>":[23],"[d":[24],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u0393</sub>":[27,33,47],"(v)":[28,48],"+":[29],"d":[30,44],"(w)]":[34],"<sup":[35],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u03b2</sup>":[37],",":[38],"where":[39,139],"\u03b2":[40,120],"\u2208":[41,121,141],"R":[42],"and":[43,68,84,108,126,151],"denotes":[49],"degree":[51],"of":[52,63,76,95,131,155,168],"vertex":[54],"v":[55],"in":[56,79],"\u0393.":[60],"The":[61],"problem":[62],"finding":[64],"best":[65],"possible":[66],"upper":[67],"lower":[69],"bound":[70],"for":[71,99,119,136,172],"certain":[72],"topological":[73],"fundamental":[77],"nature":[78],"extremal":[80],"theory.":[82],"Akhtar":[83],"Imran":[85],"[J.":[86],"Inequal.":[87],"Appl.":[88,111],"(2016)":[89],"241]":[90],"obtained":[91,165],"sharp":[93,129,160],"bounds":[94,130,157],"four":[100],"operations":[102],"(F-sum":[103],"graphs)":[104],"introduced":[105],"by":[106],"Eliasi":[107],"Taeri":[109],"[Discrete":[110],"Math.":[112],"157:":[113],"794-803,":[114],"2009)].":[115],"In":[116,162],"this":[117],"paper,":[118],"N,":[122],"we":[123,164],"figured":[124],"out":[125],"improved":[127,156],"F-sum":[137,173],"graphs,":[138,174],"F":[140,176],"{R,":[142],"Q,":[143],"T}.":[144],"Several":[145],"examples":[146],"are":[147],"presented":[148],"to":[149],"elaborate":[150],"compare":[152],"results":[154],"with":[158],"existing":[159],"bounds.":[161],"addition,":[163],"exact":[166],"formula":[167],"when":[175],"S.":[178]},"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":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
