{"id":"https://openalex.org/W2952511300","doi":"https://doi.org/10.37236/1021","title":"The Spectral Radius of Subgraphs of Regular Graphs","display_name":"The Spectral Radius of Subgraphs of Regular Graphs","publication_year":2007,"publication_date":"2007-10-05","ids":{"openalex":"https://openalex.org/W2952511300","doi":"https://doi.org/10.37236/1021","mag":"2952511300"},"language":"en","primary_location":{"id":"doi:10.37236/1021","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1021","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v14i1n20/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v14i1n20/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5114376809","display_name":"Vladimir Nikiforov","orcid":"https://orcid.org/0000-0003-4860-5407"},"institutions":[{"id":"https://openalex.org/I94658018","display_name":"University of Memphis","ror":"https://ror.org/01cq23130","country_code":"US","type":"education","lineage":["https://openalex.org/I94658018"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Vladimir Nikiforov","raw_affiliation_strings":["Department of Mathematical Sciences, University of Memphis, Memphis TN 38152, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, University of Memphis, Memphis TN 38152, USA","institution_ids":["https://openalex.org/I94658018"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5114376809"],"corresponding_institution_ids":["https://openalex.org/I94658018"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.365317,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","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":0.9998999834060669,"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":0.9998999834060669,"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":0.9983000159263611,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9944999814033508,"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/spectral-radius","display_name":"Spectral radius","score":0.8686946630477905},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6829779148101807},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6653921008110046},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6000707149505615},{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.5518317818641663},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5510561466217041},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.547620952129364},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5221917033195496},{"id":"https://openalex.org/keywords/strongly-regular-graph","display_name":"Strongly regular graph","score":0.4311100244522095},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3633134961128235},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20493638515472412},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.16370835900306702},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1567808985710144},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.0923624336719513},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07040637731552124},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.05431279540061951},{"id":"https://openalex.org/keywords/computer-network","display_name":"Computer network","score":0.04810148477554321}],"concepts":[{"id":"https://openalex.org/C140532419","wikidata":"https://www.wikidata.org/wiki/Q249748","display_name":"Spectral radius","level":3,"score":0.8686946630477905},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6829779148101807},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6653921008110046},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6000707149505615},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.5518317818641663},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5510561466217041},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.547620952129364},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5221917033195496},{"id":"https://openalex.org/C133875400","wikidata":"https://www.wikidata.org/wiki/Q692823","display_name":"Strongly regular graph","level":5,"score":0.4311100244522095},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3633134961128235},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20493638515472412},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.16370835900306702},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1567808985710144},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.0923624336719513},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07040637731552124},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.05431279540061951},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.04810148477554321},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.37236/1021","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1021","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v14i1n20/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:0705.3457","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0705.3457","pdf_url":"https://arxiv.org/pdf/0705.3457","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2952511300","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/0705.3457","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.178.5395","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.178.5395","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_14/PDF/v14i1n20.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.246.3561","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.246.3561","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0705.3457v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.545.8355","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.545.8355","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://umdrive.memphis.edu/vnikifrv/public/pdfs/Ni07g.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.0705.3457","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.0705.3457","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.37236/1021","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1021","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v14i1n20/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2952511300.pdf","grobid_xml":"https://content.openalex.org/works/W2952511300.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W2134034033","https://openalex.org/W2610857016","https://openalex.org/W2999046549"],"related_works":["https://openalex.org/W2280110976","https://openalex.org/W2080350485","https://openalex.org/W2358795979","https://openalex.org/W2379926271","https://openalex.org/W3191908787","https://openalex.org/W2022302905","https://openalex.org/W2311538476","https://openalex.org/W2367861819","https://openalex.org/W2794355847","https://openalex.org/W2066487333","https://openalex.org/W2384426183","https://openalex.org/W3155548670","https://openalex.org/W2916099937","https://openalex.org/W2051100137","https://openalex.org/W2367720302","https://openalex.org/W2368422477","https://openalex.org/W2385859608","https://openalex.org/W3081099320","https://openalex.org/W2370878148","https://openalex.org/W2364188840"],"abstract_inverted_index":{"Let":[0,27],"$\\mu\\left(":[1],"G\\right)":[2,6,51,75,77],"$":[3,7],"and":[4,11,36,68],"$\\mu_{\\min}\\left(":[5],"be":[8,29],"the":[9,15],"largest":[10],"smallest":[12],"eigenvalues":[13],"of":[14,18,33,46,65],"adjacency":[16],"matrix":[17],"a":[19,30,43,61],"graph":[20,32,64],"$G$.":[21],"Our":[22],"main":[23],"results":[24],"are:":[25],"(i)":[26],"$G$":[28,59],"regular":[31,62],"order":[34,66],"$n$":[35,67],"finite":[37,69],"diameter":[38,70],"$D.$":[39],"If":[40,58],"$H$":[41],"is":[42,60],"proper":[44],"subgraph":[45],"$G,$":[47],"then":[48,72],"$$":[49,56,73,80],"\\mu\\left(":[50,74],"-\\mu\\left(":[52],"H\\right)":[53],"&gt;{1\\over":[54,78],"nD}.":[55,79],"(ii)":[57],"nonbipartite":[63],"$D$,":[71],"+\\mu_{\\min}\\left(":[76]},"counts_by_year":[],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}
