{"id":"https://openalex.org/W1528275408","doi":"https://doi.org/10.37236/387","title":"On Sum of Powers of the Laplacian and Signless Laplacian Eigenvalues of Graphs","display_name":"On Sum of Powers of the Laplacian and Signless Laplacian Eigenvalues of Graphs","publication_year":2010,"publication_date":"2010-08-16","ids":{"openalex":"https://openalex.org/W1528275408","doi":"https://doi.org/10.37236/387","mag":"1528275408"},"language":"en","primary_location":{"id":"doi:10.37236/387","is_oa":true,"landing_page_url":"https://doi.org/10.37236/387","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r115/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":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r115/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060541368","display_name":"Saieed Akbari","orcid":"https://orcid.org/0000-0001-8994-8858"},"institutions":[{"id":"https://openalex.org/I133529467","display_name":"Sharif University of Technology","ror":"https://ror.org/024c2fq17","country_code":"IR","type":"education","lineage":["https://openalex.org/I133529467"]},{"id":"https://openalex.org/I4210146419","display_name":"Institute for Research in Fundamental Sciences","ror":"https://ror.org/04xreqs31","country_code":"IR","type":"facility","lineage":["https://openalex.org/I4210146419"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Saieed Akbari","raw_affiliation_strings":["Department of Mathematical Sciences Sharif University of Technology P.O. Box 11155-9415, Tehran, Iran","School of Mathematics Institute for Research in Fundamental Sciences (IPM) P.O. Box 19395-5746, Tehran, Iran","Sharif University of Technology"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences Sharif University of Technology P.O. Box 11155-9415, Tehran, Iran","institution_ids":["https://openalex.org/I133529467"]},{"raw_affiliation_string":"School of Mathematics Institute for Research in Fundamental Sciences (IPM) P.O. Box 19395-5746, Tehran, Iran","institution_ids":["https://openalex.org/I4210146419"]},{"raw_affiliation_string":"Sharif University of Technology","institution_ids":["https://openalex.org/I133529467"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008547727","display_name":"Ebrahim Ghorbani","orcid":"https://orcid.org/0000-0001-7195-8601"},"institutions":[{"id":"https://openalex.org/I133529467","display_name":"Sharif University of Technology","ror":"https://ror.org/024c2fq17","country_code":"IR","type":"education","lineage":["https://openalex.org/I133529467"]},{"id":"https://openalex.org/I4210146419","display_name":"Institute for Research in Fundamental Sciences","ror":"https://ror.org/04xreqs31","country_code":"IR","type":"facility","lineage":["https://openalex.org/I4210146419"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Ebrahim Ghorbani","raw_affiliation_strings":["Department of Mathematical Sciences Sharif University of Technology P.O. Box 11155-9415, Tehran, Iran","School of Mathematics Institute for Research in Fundamental Sciences (IPM) P.O. Box 19395-5746, Tehran, Iran","Sharif University of Technology"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences Sharif University of Technology P.O. Box 11155-9415, Tehran, Iran","institution_ids":["https://openalex.org/I133529467"]},{"raw_affiliation_string":"School of Mathematics Institute for Research in Fundamental Sciences (IPM) P.O. Box 19395-5746, Tehran, Iran","institution_ids":["https://openalex.org/I4210146419"]},{"raw_affiliation_string":"Sharif University of Technology","institution_ids":["https://openalex.org/I133529467"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048096758","display_name":"Jack H. Koolen","orcid":"https://orcid.org/0000-0002-8623-5681"},"institutions":[{"id":"https://openalex.org/I133529467","display_name":"Sharif University of Technology","ror":"https://ror.org/024c2fq17","country_code":"IR","type":"education","lineage":["https://openalex.org/I133529467"]},{"id":"https://openalex.org/I123900574","display_name":"Pohang University of Science and Technology","ror":"https://ror.org/04xysgw12","country_code":"KR","type":"education","lineage":["https://openalex.org/I123900574"]}],"countries":["IR","KR"],"is_corresponding":false,"raw_author_name":"Jacobus H. Koolen","raw_affiliation_strings":["Department of Mathematics Pohang University of Science and Technology (POSTECH) Pohang 790-785, South Korea","Pohang Mathematics Institute (PMI) Pohang University of Science and Technology (POSTECH) Pohang 790-785, South Korea","Sharif University of Technology"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Pohang University of Science and Technology (POSTECH) Pohang 790-785, South Korea","institution_ids":["https://openalex.org/I123900574"]},{"raw_affiliation_string":"Pohang Mathematics Institute (PMI) Pohang University of Science and Technology (POSTECH) Pohang 790-785, South Korea","institution_ids":["https://openalex.org/I123900574"]},{"raw_affiliation_string":"Sharif University of Technology","institution_ids":["https://openalex.org/I133529467"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015969326","display_name":"Mohammad Reza Oboudi","orcid":"https://orcid.org/0000-0003-3997-2600"},"institutions":[{"id":"https://openalex.org/I133529467","display_name":"Sharif University of Technology","ror":"https://ror.org/024c2fq17","country_code":"IR","type":"education","lineage":["https://openalex.org/I133529467"]},{"id":"https://openalex.org/I123900574","display_name":"Pohang University of Science and Technology","ror":"https://ror.org/04xysgw12","country_code":"KR","type":"education","lineage":["https://openalex.org/I123900574"]},{"id":"https://openalex.org/I4210146419","display_name":"Institute for Research in Fundamental Sciences","ror":"https://ror.org/04xreqs31","country_code":"IR","type":"facility","lineage":["https://openalex.org/I4210146419"]}],"countries":["IR","KR"],"is_corresponding":false,"raw_author_name":"Mohammad Reza Oboudi","raw_affiliation_strings":["Department of Mathematical Sciences Sharif University of Technology P.O. Box 11155-9415, Tehran, Iran","School of Mathematics Institute for Research in Fundamental Sciences (IPM) P.O. Box 19395-5746, Tehran, Iran","Pohang University of Science and Technology"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences Sharif University of Technology P.O. Box 11155-9415, Tehran, Iran","institution_ids":["https://openalex.org/I133529467"]},{"raw_affiliation_string":"School of Mathematics Institute for Research in Fundamental Sciences (IPM) P.O. Box 19395-5746, Tehran, Iran","institution_ids":["https://openalex.org/I4210146419"]},{"raw_affiliation_string":"Pohang University of Science and Technology","institution_ids":["https://openalex.org/I123900574"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5060541368"],"corresponding_institution_ids":["https://openalex.org/I133529467","https://openalex.org/I4210146419"],"apc_list":null,"apc_paid":null,"fwci":5.5886,"has_fulltext":true,"cited_by_count":31,"citation_normalized_percentile":{"value":0.96279826,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"17","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":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":0.9853000044822693,"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/T10612","display_name":"Magnetism in coordination complexes","score":0.9643999934196472,"subfield":{"id":"https://openalex.org/subfields/2504","display_name":"Electronic, Optical and Magnetic Materials"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8832421898841858},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.7931214570999146},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7443203926086426},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7009226083755493},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.6295928955078125},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5597507357597351},{"id":"https://openalex.org/keywords/beta","display_name":"BETA (programming language)","score":0.5186911821365356},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4971294701099396},{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.42909711599349976},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17093059420585632},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07698759436607361},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.042788565158843994}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8832421898841858},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.7931214570999146},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7443203926086426},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7009226083755493},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.6295928955078125},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5597507357597351},{"id":"https://openalex.org/C2776174256","wikidata":"https://www.wikidata.org/wiki/Q830842","display_name":"BETA (programming language)","level":2,"score":0.5186911821365356},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4971294701099396},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.42909711599349976},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17093059420585632},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07698759436607361},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.042788565158843994},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","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},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/387","is_oa":true,"landing_page_url":"https://doi.org/10.37236/387","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r115/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:CiteSeerX.psu:10.1.1.176.3812","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.176.3812","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_17/PDF/v17i1r115.pdf","raw_type":"text"},{"id":"pmh:oai:oasis.postech.ac.kr:2014.oak/25569","is_oa":false,"landing_page_url":"https://oasis.postech.ac.kr/handle/2014.oak/25569","pdf_url":null,"source":{"id":"https://openalex.org/S4306401965","display_name":"Open Access System for Information Sharing (Pohang University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I123900574","host_organization_name":"Pohang University of Science and Technology","host_organization_lineage":["https://openalex.org/I123900574"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.37236/387","is_oa":true,"landing_page_url":"https://doi.org/10.37236/387","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r115/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":[{"id":"https://openalex.org/G3034753964","display_name":null,"funder_award_id":"grant","funder_id":"https://openalex.org/F4320320671","funder_display_name":"National Research Foundation"},{"id":"https://openalex.org/G342704958","display_name":null,"funder_award_id":"funded","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"},{"id":"https://openalex.org/G7106934242","display_name":null,"funder_award_id":"2009-0094069","funder_id":"https://openalex.org/F4320322349","funder_display_name":"Ministry of Education, Science and Technology"}],"funders":[{"id":"https://openalex.org/F4320320671","display_name":"National Research Foundation","ror":"https://ror.org/05s0g1g46"},{"id":"https://openalex.org/F4320321282","display_name":"Pohang University of Science and Technology","ror":"https://ror.org/04xysgw12"},{"id":"https://openalex.org/F4320322120","display_name":"National Research Foundation of Korea","ror":"https://ror.org/013aysd81"},{"id":"https://openalex.org/F4320322349","display_name":"Ministry of Education, Science and Technology","ror":"https://ror.org/01p262204"},{"id":"https://openalex.org/F4320323627","display_name":"School of Mathematics, Institute for Research in Fundamental Sciences","ror":"https://ror.org/04xreqs31"},{"id":"https://openalex.org/F4320323645","display_name":"Institute for Research in Fundamental Sciences","ror":"https://ror.org/04xreqs31"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1528275408.pdf","grobid_xml":"https://content.openalex.org/works/W1528275408.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W1507693993","https://openalex.org/W1515707356","https://openalex.org/W1977317053","https://openalex.org/W1992830358","https://openalex.org/W2001755625","https://openalex.org/W2008751510","https://openalex.org/W2036527841","https://openalex.org/W2120940840","https://openalex.org/W2123349990","https://openalex.org/W2146232410","https://openalex.org/W2150536463","https://openalex.org/W2158551910","https://openalex.org/W2182831171","https://openalex.org/W2479778494","https://openalex.org/W2610857016","https://openalex.org/W4205875772","https://openalex.org/W4285719527","https://openalex.org/W4402135571","https://openalex.org/W6601365606","https://openalex.org/W6638553918"],"related_works":["https://openalex.org/W154856185","https://openalex.org/W2383428243","https://openalex.org/W4380570985","https://openalex.org/W2570009360","https://openalex.org/W3004345458","https://openalex.org/W2883186538","https://openalex.org/W2051180862","https://openalex.org/W1976439244","https://openalex.org/W2402951419","https://openalex.org/W2896947499"],"abstract_inverted_index":{"Let":[0],"$G$":[1,74],"be":[2],"a":[3],"graph":[4],"of":[5],"order":[6],"$n$":[7],"with":[8,27,47],"signless":[9],"Laplacian":[10,15],"eigenvalues":[11,16],"$q_1,":[12],"\\ldots,q_n$":[13],"and":[14,41,71],"$\\mu_1,\\ldots,\\mu_n$.":[17],"It":[18],"is":[19,64,75],"proved":[20],"that":[21],"for":[22,42],"any":[23,43],"real":[24,44],"number":[25,45],"$\\alpha$":[26],"$0":[28],"&lt;":[29,33,49,51],"\\alpha\\leq1$":[30],"or":[31],"$2\\leq\\alpha":[32],"3$,":[34],"the":[35,53,62],"inequality":[36,54],"$q_1^\\alpha+\\cdots+":[37],"q_n^\\alpha\\geq":[38],"\\mu_1^\\alpha+\\cdots+\\mu_n^\\alpha$":[39],"holds,":[40],"$\\beta$":[46],"$1":[48],"\\beta":[50],"2$,":[52],"$q_1^\\beta+\\cdots+":[55],"q_n^\\beta\\le":[56],"\\mu_1^\\beta+\\cdots+\\mu_n^\\beta$":[57],"holds.":[58],"In":[59],"both":[60],"inequalities,":[61],"equality":[63],"attained":[65],"(for":[66],"$\\alpha":[67],"\\notin":[68],"\\{1,2\\}$)":[69],"if":[70,73],"only":[72],"bipartite.":[76]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":13}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
