{"id":"https://openalex.org/W4303981694","doi":"https://doi.org/10.1142/s1793830922501713","title":"Tensor products and strong products of soft graphs","display_name":"Tensor products and strong products of soft graphs","publication_year":2022,"publication_date":"2022-10-10","ids":{"openalex":"https://openalex.org/W4303981694","doi":"https://doi.org/10.1142/s1793830922501713"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830922501713","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830922501713","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072115851","display_name":"Bobin George","orcid":"https://orcid.org/0000-0002-2477-6220"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bobin George","raw_affiliation_strings":["Department of Mathematics, Pavanatma College Murickassery, Kerala, India"],"raw_orcid":"https://orcid.org/0000-0002-2477-6220","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Pavanatma College Murickassery, Kerala, India","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019251337","display_name":"Jinta Jose","orcid":"https://orcid.org/0000-0002-3743-2945"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jinta Jose","raw_affiliation_strings":["Department of Science and Humanities, Viswajyothi College of Engineering and Technology, Vazhakulam, Kerala, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Science and Humanities, Viswajyothi College of Engineering and Technology, Vazhakulam, Kerala, India","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055128902","display_name":"Rajesh K. Thumbakara","orcid":"https://orcid.org/0000-0001-7503-8861"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rajesh K. Thumbakara","raw_affiliation_strings":["Department of Mathematics, Mar Athanasius College Kothamangalam, Kerala, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Mar Athanasius College Kothamangalam, Kerala, India","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5072115851"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.5596,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.93243069,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"15","issue":"08","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11671","display_name":"Fuzzy and Soft Set Theory","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9107999801635742,"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/graph-product","display_name":"Graph product","score":0.7381834983825684},{"id":"https://openalex.org/keywords/soft-set","display_name":"Soft set","score":0.5380629301071167},{"id":"https://openalex.org/keywords/indifference-graph","display_name":"Indifference graph","score":0.4965417981147766},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.4961720407009125},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.4466439187526703},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.440384179353714},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.4264034628868103},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41962820291519165},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40295249223709106},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.34819719195365906},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3160032629966736},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.26615607738494873},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.0981384813785553},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.0793943703174591}],"concepts":[{"id":"https://openalex.org/C68103157","wikidata":"https://www.wikidata.org/wiki/Q569347","display_name":"Graph product","level":5,"score":0.7381834983825684},{"id":"https://openalex.org/C2777037408","wikidata":"https://www.wikidata.org/wiki/Q4310193","display_name":"Soft set","level":3,"score":0.5380629301071167},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.4965417981147766},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.4961720407009125},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.4466439187526703},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.440384179353714},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.4264034628868103},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41962820291519165},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40295249223709106},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.34819719195365906},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3160032629966736},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.26615607738494873},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0981384813785553},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0793943703174591},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830922501713","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830922501713","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7400000095367432,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1495288901","https://openalex.org/W1978352585","https://openalex.org/W1982907249","https://openalex.org/W2191274632","https://openalex.org/W2315241089","https://openalex.org/W2490805901","https://openalex.org/W2891384280","https://openalex.org/W2975796134","https://openalex.org/W3047429704","https://openalex.org/W4293773017"],"related_works":["https://openalex.org/W4220852510","https://openalex.org/W603403972","https://openalex.org/W4287749642","https://openalex.org/W1919313975","https://openalex.org/W3130332934","https://openalex.org/W3038621866","https://openalex.org/W2075637037","https://openalex.org/W3168576739","https://openalex.org/W2362011785","https://openalex.org/W2522664322"],"abstract_inverted_index":{"Molodtsov":[0],"developed":[1],"soft":[2,19,39,96,119,127,131],"set":[3,20],"theory":[4,21,43,51],"in":[5,49,149],"1999":[6],"as":[7],"an":[8],"approach":[9],"for":[10,31,137],"modeling":[11],"vagueness":[12],"and":[13,113,133,143],"uncertainty.":[14],"Many":[15],"academics":[16],"currently":[17],"employ":[18],"to":[22,56,84],"solve":[23],"decision-making":[24],"problems.":[25],"A":[26],"parameterized":[27],"point":[28],"of":[29,38,53,64,87,118,126,146],"view":[30],"graphs":[32,77,128],"is":[33,44,72],"provided":[34],"using":[35],"the":[36,62,85,103,106,110,114,144],"idea":[37],"graphs.":[40,97,120],"Soft":[41],"graph":[42,50,60,65,88],"a":[45,73],"rapidly":[46],"growing":[47],"field":[48],"because":[52],"its":[54],"adaptability":[55],"parameterization":[57],"techniques.":[58],"In":[59,98],"theory,":[61],"topic":[63],"products":[66,125],"has":[67,79],"attracted":[68],"much":[69],"attention.":[70],"It":[71],"binary":[74],"operation":[75],"on":[76,95],"that":[78,123],"many":[80],"combinatorial":[81],"applications.":[82],"Analogous":[83],"definitions":[86],"products,":[89],"we":[90,101,134],"can":[91],"define":[92],"product":[93,117],"operations":[94],"this":[99],"paper,":[100],"introduce":[102],"tensor":[104,108],"product,":[105,109,112],"restricted":[107,115],"strong":[111,116],"We":[121],"prove":[122],"these":[124],"are":[129],"also":[130],"graphs,":[132],"derive":[135],"formulas":[136],"finding":[138],"vertex":[139],"count,":[140,142],"edge":[141],"sum":[145],"part":[147],"degrees":[148],"them.":[150]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":14},{"year":2023,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
