{"id":"https://openalex.org/W4306884996","doi":"https://doi.org/10.1142/s1793830922501749","title":"Independence number and the normalized Laplacian eigenvalue one","display_name":"Independence number and the normalized Laplacian eigenvalue one","publication_year":2022,"publication_date":"2022-10-20","ids":{"openalex":"https://openalex.org/W4306884996","doi":"https://doi.org/10.1142/s1793830922501749"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830922501749","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830922501749","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/A5038372202","display_name":"Arpita Das","orcid":"https://orcid.org/0000-0002-5939-2382"},"institutions":[{"id":"https://openalex.org/I145894827","display_name":"Indian Institute of Technology Kharagpur","ror":"https://ror.org/03w5sq511","country_code":"IN","type":"education","lineage":["https://openalex.org/I145894827"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Arpita Das","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Technology Kharagpur, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Kharagpur, India","institution_ids":["https://openalex.org/I145894827"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058224920","display_name":"Pratima Panigrahi","orcid":"https://orcid.org/0009-0004-0330-3258"},"institutions":[{"id":"https://openalex.org/I145894827","display_name":"Indian Institute of Technology Kharagpur","ror":"https://ror.org/03w5sq511","country_code":"IN","type":"education","lineage":["https://openalex.org/I145894827"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Pratima Panigrahi","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Technology Kharagpur, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Kharagpur, India","institution_ids":["https://openalex.org/I145894827"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5038372202"],"corresponding_institution_ids":["https://openalex.org/I145894827"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.19775281,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"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/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/T11298","display_name":"Synthesis and Properties of Aromatic Compounds","score":0.9980000257492065,"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"}},{"id":"https://openalex.org/T10096","display_name":"Metal-Organic Frameworks: Synthesis and Applications","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/1604","display_name":"Inorganic 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/independence-number","display_name":"Independence number","score":0.7320073843002319},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6996004581451416},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6913695335388184},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.6471604108810425},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6079486608505249},{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.5483466386795044},{"id":"https://openalex.org/keywords/multiplicity","display_name":"Multiplicity (mathematics)","score":0.5448125004768372},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5068867802619934},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4583948850631714},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35036495327949524},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16287937760353088},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1607772409915924},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07582885026931763}],"concepts":[{"id":"https://openalex.org/C2984853995","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independence number","level":3,"score":0.7320073843002319},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6996004581451416},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6913695335388184},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.6471604108810425},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6079486608505249},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.5483466386795044},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.5448125004768372},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5068867802619934},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4583948850631714},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35036495327949524},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16287937760353088},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1607772409915924},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07582885026931763},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830922501749","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830922501749","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1488435683","https://openalex.org/W2076293993","https://openalex.org/W2089453317","https://openalex.org/W2135650427","https://openalex.org/W2478475484","https://openalex.org/W2515643324","https://openalex.org/W2767851607","https://openalex.org/W4237658155","https://openalex.org/W4238591275","https://openalex.org/W4300427762"],"related_works":["https://openalex.org/W2966420163","https://openalex.org/W3044150289","https://openalex.org/W2031498676","https://openalex.org/W4287549458","https://openalex.org/W3117819834","https://openalex.org/W1832592836","https://openalex.org/W4293876796","https://openalex.org/W3191322565","https://openalex.org/W3132233781","https://openalex.org/W2162396328"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,50],"prove":[4],"that":[5],"every":[6],"simple":[7],"connected":[8],"graph":[9],"with":[10,23,53],"[Formula:":[11,15,27,31,35,54,62],"see":[12,16,28,32,36,55,63],"text]":[13,17,33,37,56,64],"has":[14],"as":[18,65],"a":[19,66],"normalized":[20,67],"Laplacian":[21,68],"eigenvalue":[22],"multiplicity":[24],"at":[25],"least":[26],"text],":[29],"where":[30],"and":[34,41,57],"are":[38],"the":[39,42,46],"order":[40],"independence":[43],"number":[44],"of":[45],"graph,":[47],"respectively.":[48],"Then":[49],"investigate":[51],"graphs":[52],"having":[58,61],"or":[59],"not":[60],"eigenvalue.":[69]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
