{"id":"https://openalex.org/W3084611484","doi":"https://doi.org/10.1142/s1793830921500191","title":"Weighted PI index of tensor product and strong product of graphs","display_name":"Weighted PI index of tensor product and strong product of graphs","publication_year":2020,"publication_date":"2020-09-10","ids":{"openalex":"https://openalex.org/W3084611484","doi":"https://doi.org/10.1142/s1793830921500191","mag":"3084611484"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830921500191","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830921500191","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/A5066527789","display_name":"C. Gopika","orcid":null},"institutions":[{"id":"https://openalex.org/I81556334","display_name":"Amrita Vishwa Vidyapeetham","ror":"https://ror.org/03am10p12","country_code":"IN","type":"education","lineage":["https://openalex.org/I81556334"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"C. Gopika","raw_affiliation_strings":["Department of Mathematics, Amrita School of Engineering, Coimbatore, Amrita Vishwa Vidyapeetham, Coimbatore, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Amrita School of Engineering, Coimbatore, Amrita Vishwa Vidyapeetham, Coimbatore, India","institution_ids":["https://openalex.org/I81556334"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102780127","display_name":"J. Geetha","orcid":"https://orcid.org/0000-0003-0558-5389"},"institutions":[{"id":"https://openalex.org/I81556334","display_name":"Amrita Vishwa Vidyapeetham","ror":"https://ror.org/03am10p12","country_code":"IN","type":"education","lineage":["https://openalex.org/I81556334"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"J. Geetha","raw_affiliation_strings":["Department of Mathematics, Amrita School of Engineering, Coimbatore, Amrita Vishwa Vidyapeetham, Coimbatore, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Amrita School of Engineering, Coimbatore, Amrita Vishwa Vidyapeetham, Coimbatore, India","institution_ids":["https://openalex.org/I81556334"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026730702","display_name":"K. Somasundaram","orcid":"https://orcid.org/0000-0003-2226-1845"},"institutions":[{"id":"https://openalex.org/I81556334","display_name":"Amrita Vishwa Vidyapeetham","ror":"https://ror.org/03am10p12","country_code":"IN","type":"education","lineage":["https://openalex.org/I81556334"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"K. Somasundaram","raw_affiliation_strings":["Department of Mathematics, Amrita School of Engineering, Coimbatore, Amrita Vishwa Vidyapeetham, Coimbatore, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Amrita School of Engineering, Coimbatore, Amrita Vishwa Vidyapeetham, Coimbatore, India","institution_ids":["https://openalex.org/I81556334"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5102780127"],"corresponding_institution_ids":["https://openalex.org/I81556334"],"apc_list":null,"apc_paid":null,"fwci":1.1556,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.77352941,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"13","issue":"03","first_page":"2150019","last_page":"2150019"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":1.0,"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":1.0,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9959999918937683,"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":0.9937999844551086,"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/equidistant","display_name":"Equidistant","score":0.7225277423858643},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.6909337043762207},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6886876225471497},{"id":"https://openalex.org/keywords/pi","display_name":"Pi","score":0.6536901593208313},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6396608352661133},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5671538710594177},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5394178032875061},{"id":"https://openalex.org/keywords/index","display_name":"Index (typography)","score":0.48870518803596497},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4441555440425873},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.4302121102809906},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34755939245224},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19933173060417175},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1579533815383911},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12556713819503784}],"concepts":[{"id":"https://openalex.org/C158245278","wikidata":"https://www.wikidata.org/wiki/Q4386982","display_name":"Equidistant","level":2,"score":0.7225277423858643},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.6909337043762207},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6886876225471497},{"id":"https://openalex.org/C53009064","wikidata":"https://www.wikidata.org/wiki/Q167","display_name":"Pi","level":2,"score":0.6536901593208313},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6396608352661133},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5671538710594177},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5394178032875061},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.48870518803596497},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4441555440425873},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.4302121102809906},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34755939245224},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19933173060417175},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1579533815383911},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12556713819503784},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"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":1,"locations":[{"id":"doi:10.1142/s1793830921500191","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830921500191","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":0.4399999976158142,"id":"https://metadata.un.org/sdg/8","display_name":"Decent work and economic growth"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1966739396","https://openalex.org/W1977471756","https://openalex.org/W1988447874","https://openalex.org/W2014998080","https://openalex.org/W2028907980","https://openalex.org/W2064206595","https://openalex.org/W2510541366","https://openalex.org/W2884117239"],"related_works":["https://openalex.org/W38971153","https://openalex.org/W2555302402","https://openalex.org/W3197048833","https://openalex.org/W4301892171","https://openalex.org/W2078648404","https://openalex.org/W2180632820","https://openalex.org/W2963026927","https://openalex.org/W3125752994","https://openalex.org/W1990960175","https://openalex.org/W2000144448"],"abstract_inverted_index":{"The":[0],"Weighted":[1],"Padmakar\u2013Ivan":[2],"(PI)":[3],"index":[4,40],"of":[5,26,29,41,47],"a":[6],"connected,":[7],"simple":[8],"graph":[9],"[Formula:":[10,16,20,32],"see":[11,17,21,33],"text]":[12,22],"is":[13],"given":[14],"by":[15],"text],":[18],"where":[19],"denotes":[23],"the":[24,30],"number":[25],"equidistant":[27],"vertices":[28],"edge":[31],"text].":[34],"In":[35],"this":[36],"paper,":[37],"weighted":[38],"PI":[39],"tensor":[42],"product":[43,46],"and":[44],"strong":[45],"some":[48],"graphs":[49],"are":[50],"obtained.":[51]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}