{"id":"https://openalex.org/W4295094777","doi":"https://doi.org/10.1155/2022/6288054","title":"Computation of the Complexity of Networks under Generalized Operations","display_name":"Computation of the Complexity of Networks under Generalized Operations","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4295094777","doi":"https://doi.org/10.1155/2022/6288054"},"language":"en","primary_location":{"id":"doi:10.1155/2022/6288054","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/6288054","pdf_url":"https://downloads.hindawi.com/journals/complexity/2022/6288054.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/2022/6288054.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074332972","display_name":"Hafiz Usman Afzal","orcid":"https://orcid.org/0000-0003-0817-8260"},"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":"Hafiz Usman Afzal","raw_affiliation_strings":["Department of Mathematics, School of Science, University of Management and Technology, Lahore 54770"],"raw_orcid":"https://orcid.org/0000-0003-0817-8260","affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Science, University of Management and Technology, Lahore 54770","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 54770, Pakistan","Department of Mathematics, School of Science, University of Management and Technology, Lahore 54770"],"raw_orcid":"https://orcid.org/0000-0001-7241-8172","affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Science, University of Management and Technology, Lahore 54770, Pakistan","institution_ids":["https://openalex.org/I87482320"]},{"raw_affiliation_string":"Department of Mathematics, School of Science, University of Management and Technology, Lahore 54770","institution_ids":["https://openalex.org/I87482320"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047307438","display_name":"Ali Ovais","orcid":"https://orcid.org/0000-0002-4909-3418"},"institutions":[{"id":"https://openalex.org/I142732210","display_name":"University of Engineering and Technology Lahore","ror":"https://ror.org/0051w2v06","country_code":"PK","type":"education","lineage":["https://openalex.org/I142732210"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Ali Ovais","raw_affiliation_strings":["Department of Mathematics, University of Engineering and Technology, Lahore, Pakistan","Department of Mathematics, University of Engineering and Technology, Lahore"],"raw_orcid":"https://orcid.org/0000-0002-4909-3418","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Engineering and Technology, Lahore, Pakistan","institution_ids":["https://openalex.org/I142732210"]},{"raw_affiliation_string":"Department of Mathematics, University of Engineering and Technology, Lahore","institution_ids":["https://openalex.org/I142732210"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056864680","display_name":"Md. Nur Alam","orcid":"https://orcid.org/0000-0001-6815-678X"},"institutions":[{"id":"https://openalex.org/I260446899","display_name":"Pabna University of Science and Technology","ror":"https://ror.org/01vxg3438","country_code":"BD","type":"education","lineage":["https://openalex.org/I260446899"]}],"countries":["BD"],"is_corresponding":true,"raw_author_name":"Md Nur Alam","raw_affiliation_strings":["Department of Mathematics, Pabna University of Science and Technology, Pabna 6600"],"raw_orcid":"https://orcid.org/0000-0001-6815-678X","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Pabna University of Science and Technology, Pabna 6600","institution_ids":["https://openalex.org/I260446899"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5056864680"],"corresponding_institution_ids":["https://openalex.org/I260446899"],"apc_list":{"value":2550,"currency":"USD","value_usd":2550},"apc_paid":{"value":2550,"currency":"USD","value_usd":2550},"fwci":0.759,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.68229909,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"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":0.9993000030517578,"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":0.9993000030517578,"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.9900000095367432,"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"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9763000011444092,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4481913447380066},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3622361123561859},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.328147292137146}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4481913447380066},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3622361123561859},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.328147292137146}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2022/6288054","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/6288054","pdf_url":"https://downloads.hindawi.com/journals/complexity/2022/6288054.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:6288054","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/complexity/2022/6288054.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:f418486707cc4c76bc518c29a4a8bcd9","is_oa":true,"landing_page_url":"https://doaj.org/article/f418486707cc4c76bc518c29a4a8bcd9","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 2022 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2022/6288054","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/6288054","pdf_url":"https://downloads.hindawi.com/journals/complexity/2022/6288054.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":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4295094777.pdf","grobid_xml":"https://content.openalex.org/works/W4295094777.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W415832010","https://openalex.org/W1570182137","https://openalex.org/W1572054018","https://openalex.org/W1888793072","https://openalex.org/W2015729136","https://openalex.org/W2029673229","https://openalex.org/W2035001841","https://openalex.org/W2064750898","https://openalex.org/W2067691662","https://openalex.org/W2476153571","https://openalex.org/W2735870192","https://openalex.org/W2807993036","https://openalex.org/W2914274778","https://openalex.org/W2969808173","https://openalex.org/W3132230117","https://openalex.org/W4249035553","https://openalex.org/W4250831670","https://openalex.org/W4255945316"],"related_works":["https://openalex.org/W2935759653","https://openalex.org/W3105167352","https://openalex.org/W54078636","https://openalex.org/W2954470139","https://openalex.org/W1501425562","https://openalex.org/W2902782467","https://openalex.org/W3084825885","https://openalex.org/W2298861036","https://openalex.org/W3148032049","https://openalex.org/W2271181815"],"abstract_inverted_index":{"The":[0,32],"connected":[1],"and":[2,109,133],"acyclic":[3],"components":[4],"contained":[5],"in":[6,34],"a":[7,20],"network":[8,21],"are":[9],"identified":[10],"by":[11,125],"the":[12,24,38,41,110,128,143,149],"computation":[13],"of":[14,19,27,40,43,112,127,130,145,151],"its":[15],"complexity,":[16],"where":[17],"complexity":[18,42],"refers":[22],"to":[23],"total":[25],"number":[26],"spanning":[28],"trees":[29],"present":[30],"within.":[31],"article":[33],"hand":[35],"deals":[36],"with":[37,115,142],"enumeration":[39],"various":[44],"networks\u2019":[45],"operations":[46],"such":[47],"as":[48],"sum":[49],"(":[50,73,101],"K":[51,58,63,66,74,78,81,85,88,91,94,97,102,106,116],"2,":[52,59,75,82,103],"n":[53,60,62,67,70,76,83,89,95,104,114],"+":[54,61,68],"W":[55],"3":[56],",":[57,65,80,87,93],"1":[64],"S":[69,113],"),":[71,99,108],"product":[72],"\u22a0":[77,96],"2":[79,86,92,98,107,117],"\u22c9":[84],"\u00d7":[90],"difference":[100],"\u2296":[105],"conjunction":[111],".":[118],"All":[119],"our":[120],"computations":[121],"have":[122],"been":[123],"concluded":[124],"implementation":[126],"methods":[129],"linear":[131],"algebra":[132],"matrix":[134],"theory.":[135],"Our":[136],"derivations":[137],"will":[138],"also":[139],"be":[140],"highlighted":[141],"assistance":[144],"3D":[146],"plots":[147],"at":[148],"end":[150],"this":[152],"article.":[153]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}