{"id":"https://openalex.org/W1996919229","doi":"https://doi.org/10.1137/050624029","title":"The Spectrum of the Corona of Two Graphs","display_name":"The Spectrum of the Corona of Two Graphs","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W1996919229","doi":"https://doi.org/10.1137/050624029","mag":"1996919229"},"language":"en","primary_location":{"id":"doi:10.1137/050624029","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050624029","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","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/A5088230799","display_name":"Sasmita Barik","orcid":"https://orcid.org/0000-0002-3927-5218"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S. Barik","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067185431","display_name":"Sukanta Pati","orcid":"https://orcid.org/0000-0002-8995-1894"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S. Pati","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5086994569","display_name":"B. K. Sarma","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"B. K. Sarma","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7349,"has_fulltext":false,"cited_by_count":164,"citation_normalized_percentile":{"value":0.80695245,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"21","issue":"1","first_page":"47","last_page":"56"},"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/T10849","display_name":"Finite Group Theory Research","score":0.9896000027656555,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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":0.9772999882698059,"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/combinatorics","display_name":"Combinatorics","score":0.8536725044250488},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7839323878288269},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6772210001945496},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.6389080882072449},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.6376603245735168},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6296687126159668},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.5809999108314514},{"id":"https://openalex.org/keywords/multiplicity","display_name":"Multiplicity (mathematics)","score":0.5151702165603638},{"id":"https://openalex.org/keywords/spectrum","display_name":"Spectrum (functional analysis)","score":0.49136272072792053},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4529317021369934},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40498948097229004},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1510065197944641},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07411202788352966},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.05332297086715698}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8536725044250488},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7839323878288269},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6772210001945496},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.6389080882072449},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.6376603245735168},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6296687126159668},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.5809999108314514},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.5151702165603638},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.49136272072792053},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4529317021369934},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40498948097229004},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1510065197944641},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07411202788352966},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.05332297086715698}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/050624029","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050624029","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W101288343","https://openalex.org/W1587744656","https://openalex.org/W2029105623","https://openalex.org/W2051081806","https://openalex.org/W2081485118","https://openalex.org/W2082897231","https://openalex.org/W2089384997","https://openalex.org/W2107940287","https://openalex.org/W2144267444","https://openalex.org/W2171567099","https://openalex.org/W2610857016","https://openalex.org/W2799004609","https://openalex.org/W2983896310"],"related_works":["https://openalex.org/W2371352078","https://openalex.org/W2953461625","https://openalex.org/W2077383796","https://openalex.org/W2080136900","https://openalex.org/W2372768926","https://openalex.org/W2999799752","https://openalex.org/W4230581126","https://openalex.org/W2054458431","https://openalex.org/W2781442522","https://openalex.org/W2115719464"],"abstract_inverted_index":{"We":[0,144,168,198],"consider":[1],"only":[2],"simple":[3],"graphs.":[4],"Given":[5],"two":[6],"graphs":[7,174,188],"G":[8,41,55,75,100,114],"with":[9,148,175,189],"vertices":[10],"$1,\\ldots,n$":[11],"and":[12,30,42,56,76,125,151,164,193,218],"H,":[13],"the":[14,21,37,46,66,72,83,105,128,141,158,190,194,203,207,212],"corona":[15,159],"$G\\circ":[16,69,87,216],"H$":[17,70,88,217],"is":[18,89,95,101,110,117,137,157],"defined":[19],"as":[20],"graph":[22,54,59,99],"obtained":[23],"by":[24],"taking":[25],"n":[26],"copies":[27],"of":[28,40,45,49,68,74,78,86,113,120,161,172,186,211,215],"H":[29,60,94],"for":[31,131],"each":[32,43,132],"i":[33],"inserting":[34],"edges":[35],"between":[36],"ith":[38,47],"vertex":[39,44],"copy":[48],"H.":[50,79],"For":[51],"a":[52,155,170],"connected":[53],"any":[57],"r\u2010regular":[58],"we":[61,181],"provide":[62],"complete":[63],"information":[64,81],"about":[65,82,202],"spectrum":[67,73,77,85,192],"using":[71],"Complete":[80],"Laplacian":[84,196,213],"also":[90],"provided":[91],"even":[92],"when":[93],"not":[96],"regular.":[97],"A":[98],"said":[102,138],"to":[103,139,206],"have":[104,127,140],"property":[106,142,149,176],"(R)":[107],"if":[108,123],"$\\frac{1}{\\lambda}$":[109,126],"an":[111,118,165,179,220],"eigenvalue":[112,119,133,210],"whenever":[115],"$\\lambda$":[116,124],"G.":[121],"Further,":[122],"same":[129,191,195],"multiplicity,":[130],"$\\lambda$,":[134],"then":[135],"it":[136],"(SR).":[143],"characterize":[145],"all":[146],"trees":[147],"(SR)":[150],"show":[152],"that":[153],"such":[154],"tree":[156,163],"product":[160],"some":[162,200],"isolated":[166],"vertex.":[167],"supply":[169],"family":[171],"bipartite":[173],"(R).":[177],"As":[178],"application":[180],"construct":[182],"infinitely":[183],"many":[184],"pairs":[185],"nonisomorphic":[187],"spectrum.":[197],"prove":[199],"results":[201],"eigenvector":[204],"related":[205],"second":[208],"smallest":[209],"matrix":[214],"give":[219],"application.":[221]},"counts_by_year":[{"year":2026,"cited_by_count":9},{"year":2025,"cited_by_count":11},{"year":2024,"cited_by_count":14},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":15},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":14},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":19},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}