{"id":"https://openalex.org/W4281862785","doi":"https://doi.org/10.1155/2022/6927111","title":"Two Complex Graph Operations and their Exact Formulations on Topological Properties","display_name":"Two Complex Graph Operations and their Exact Formulations on Topological Properties","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4281862785","doi":"https://doi.org/10.1155/2022/6927111"},"language":"en","primary_location":{"id":"doi:10.1155/2022/6927111","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/6927111","pdf_url":"https://downloads.hindawi.com/journals/complexity/2022/6927111.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/2022/6927111.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040912593","display_name":"Shehla Hameed","orcid":"https://orcid.org/0000-0002-8370-6062"},"institutions":[{"id":"https://openalex.org/I195024194","display_name":"Riphah International University","ror":"https://ror.org/02kdm5630","country_code":"PK","type":"education","lineage":["https://openalex.org/I195024194"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Shehla Hameed","raw_affiliation_strings":["Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, Lahore, Pakistan","Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, Lahore"],"raw_orcid":"https://orcid.org/0000-0002-8370-6062","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, Lahore, Pakistan","institution_ids":["https://openalex.org/I195024194"]},{"raw_affiliation_string":"Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, Lahore","institution_ids":["https://openalex.org/I195024194"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066651205","display_name":"Muhammad Kamran Jamil","orcid":"https://orcid.org/0000-0001-5715-9299"},"institutions":[{"id":"https://openalex.org/I195024194","display_name":"Riphah International University","ror":"https://ror.org/02kdm5630","country_code":"PK","type":"education","lineage":["https://openalex.org/I195024194"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Kamran Jamil","raw_affiliation_strings":["Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, Lahore, Pakistan","Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, Lahore"],"raw_orcid":"https://orcid.org/0000-0001-5715-9299","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, Lahore, Pakistan","institution_ids":["https://openalex.org/I195024194"]},{"raw_affiliation_string":"Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, Lahore","institution_ids":["https://openalex.org/I195024194"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078254751","display_name":"Muhammad Waheed","orcid":"https://orcid.org/0000-0001-5151-5512"},"institutions":[{"id":"https://openalex.org/I195024194","display_name":"Riphah International University","ror":"https://ror.org/02kdm5630","country_code":"PK","type":"education","lineage":["https://openalex.org/I195024194"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Waheed","raw_affiliation_strings":["Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, Lahore, Pakistan","Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, Lahore"],"raw_orcid":"https://orcid.org/0000-0001-5151-5512","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, Lahore, Pakistan","institution_ids":["https://openalex.org/I195024194"]},{"raw_affiliation_string":"Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, Lahore","institution_ids":["https://openalex.org/I195024194"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023965162","display_name":"Muhammad Azeem","orcid":"https://orcid.org/0000-0001-5181-4221"},"institutions":[{"id":"https://openalex.org/I195024194","display_name":"Riphah International University","ror":"https://ror.org/02kdm5630","country_code":"PK","type":"education","lineage":["https://openalex.org/I195024194"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Azeem","raw_affiliation_strings":["Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, Lahore, Pakistan","Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, Lahore"],"raw_orcid":"https://orcid.org/0000-0001-5181-4221","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, Lahore, Pakistan","institution_ids":["https://openalex.org/I195024194"]},{"raw_affiliation_string":"Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, Lahore","institution_ids":["https://openalex.org/I195024194"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015888515","display_name":"Senesie Swaray","orcid":"https://orcid.org/0000-0003-3503-692X"},"institutions":[{"id":"https://openalex.org/I4210166695","display_name":"Sierra Leone Agricultural Research Institute","ror":"https://ror.org/05xkpwf58","country_code":"SL","type":"facility","lineage":["https://openalex.org/I4210166695"]}],"countries":["SL"],"is_corresponding":true,"raw_author_name":"Senesie Swaray","raw_affiliation_strings":["Tree Crops Unit, Sierra Leone Agricultural Research Institute, Freetown, Sierra Leone","Tree Crops Unit, Sierra Leone Agricultural Research Institute, Freetown"],"raw_orcid":"https://orcid.org/0000-0003-3503-692X","affiliations":[{"raw_affiliation_string":"Tree Crops Unit, Sierra Leone Agricultural Research Institute, Freetown, Sierra Leone","institution_ids":["https://openalex.org/I4210166695"]},{"raw_affiliation_string":"Tree Crops Unit, Sierra Leone Agricultural Research Institute, Freetown","institution_ids":["https://openalex.org/I4210166695"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5015888515"],"corresponding_institution_ids":["https://openalex.org/I4210166695"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":2.0061,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.85720306,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"2022","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":0.9998999834060669,"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":0.9998999834060669,"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":0.9945999979972839,"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/T11298","display_name":"Synthesis and Properties of Aromatic Compounds","score":0.9883999824523926,"subfield":{"id":"https://openalex.org/subfields/1605","display_name":"Organic Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/subdivision","display_name":"Subdivision","score":0.9037350416183472},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.667870044708252},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.540342390537262},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49069130420684814},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3512269854545593},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3224809765815735},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3217836022377014},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.22326838970184326}],"concepts":[{"id":"https://openalex.org/C143392562","wikidata":"https://www.wikidata.org/wiki/Q449111","display_name":"Subdivision","level":2,"score":0.9037350416183472},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.667870044708252},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.540342390537262},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49069130420684814},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3512269854545593},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3224809765815735},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3217836022377014},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.22326838970184326},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2022/6927111","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/6927111","pdf_url":"https://downloads.hindawi.com/journals/complexity/2022/6927111.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:RePEc:hin:complx:6927111","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/complexity/2022/6927111.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:a5423a2df15746bf8d4cd08e56c3c159","is_oa":false,"landing_page_url":"https://doaj.org/article/a5423a2df15746bf8d4cd08e56c3c159","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complexity, Vol 2022 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2022/6927111","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/6927111","pdf_url":"https://downloads.hindawi.com/journals/complexity/2022/6927111.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":"Sustainable cities and communities","score":0.7099999785423279,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4281862785.pdf","grobid_xml":"https://content.openalex.org/works/W4281862785.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1989537682","https://openalex.org/W2000076674","https://openalex.org/W2045993700","https://openalex.org/W2065534534","https://openalex.org/W2119446254","https://openalex.org/W2178776839","https://openalex.org/W2183841904","https://openalex.org/W2236869615","https://openalex.org/W2312056945","https://openalex.org/W2523339455","https://openalex.org/W2565779015","https://openalex.org/W2621077363","https://openalex.org/W2748887579","https://openalex.org/W2975854521","https://openalex.org/W3017987646","https://openalex.org/W3081382691","https://openalex.org/W3108702953","https://openalex.org/W3114407677","https://openalex.org/W3139176405","https://openalex.org/W3165616271","https://openalex.org/W3171985056","https://openalex.org/W4224256134","https://openalex.org/W4226439500","https://openalex.org/W4226442018","https://openalex.org/W4285295536","https://openalex.org/W6686460963"],"related_works":["https://openalex.org/W2384806462","https://openalex.org/W4389950792","https://openalex.org/W2375549870","https://openalex.org/W4376632515","https://openalex.org/W2163269603","https://openalex.org/W4205312897","https://openalex.org/W2795347481","https://openalex.org/W1106115901","https://openalex.org/W2140072033","https://openalex.org/W4248930208"],"abstract_inverted_index":{"Graph":[0],"operations":[1],"are":[2],"utilized":[3],"for":[4],"developing":[5],"complicated":[6],"graph":[7,44],"structures":[8],"from":[9],"basic":[10,14],"graphs,":[11],"and":[12,55,70,81,89],"these":[13],"graphs":[15],"can":[16],"help":[17],"to":[18],"understand":[19],"the":[20,27,30,43,67,72,82],"properties":[21],"of":[22,45,58,85],"complex":[23],"networks.":[24],"While":[25],"on":[26],"other":[28,56],"side,":[29],"topological":[31],"descriptor":[32],"is":[33,40,66],"known":[34],"as":[35],"a":[36,46],"numeric":[37],"value":[38],"that":[39],"associated":[41],"with":[42],"network.":[47],"It":[48],"has":[49],"enormous":[50],"practical":[51],"applications":[52],"in":[53,63],"chemistry":[54],"fields":[57],"science.":[59],"This":[60],"particular":[61],"work":[62,69],"this":[64],"draft":[65],"extended":[68],"investigated":[71],"first,":[73],"second,":[74],"first":[75,77],"multiplicative,":[76],"reformulated":[78],"Zagreb":[79],"indices,":[80],"forgotten":[83],"index":[84],"subdivision":[86,90],"double":[87,91],"corona":[88,93],"neighborhood":[92],"products.":[94]},"counts_by_year":[{"year":2024,"cited_by_count":4},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}