{"id":"https://openalex.org/W3032975195","doi":"https://doi.org/10.1142/s1793830920500615","title":"On distance Laplacian spectrum (energy) of graphs","display_name":"On distance Laplacian spectrum (energy) of graphs","publication_year":2020,"publication_date":"2020-06-04","ids":{"openalex":"https://openalex.org/W3032975195","doi":"https://doi.org/10.1142/s1793830920500615","mag":"3032975195"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830920500615","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830920500615","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/A5052847748","display_name":"Hilal A. Ganie","orcid":"https://orcid.org/0000-0002-2226-7828"},"institutions":[{"id":"https://openalex.org/I135388327","display_name":"University of Kashmir","ror":"https://ror.org/032xfst36","country_code":"IN","type":"education","lineage":["https://openalex.org/I135388327"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Hilal A. Ganie","raw_affiliation_strings":["Department of Mathematics, University of Kashmir, Srinagar, Kashmir, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Kashmir, Srinagar, Kashmir, India","institution_ids":["https://openalex.org/I135388327"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5052847748"],"corresponding_institution_ids":["https://openalex.org/I135388327"],"apc_list":null,"apc_paid":null,"fwci":5.7779,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.96750359,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"12","issue":"05","first_page":"2050061","last_page":"2050061"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9883999824523926,"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":0.98580002784729,"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/mathematics","display_name":"Mathematics","score":0.6494526863098145},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.6418872475624084},{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.6274098753929138},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5624954700469971},{"id":"https://openalex.org/keywords/spectrum","display_name":"Spectrum (functional analysis)","score":0.5439822673797607},{"id":"https://openalex.org/keywords/resistance-distance","display_name":"Resistance distance","score":0.5093070268630981},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4771163761615753},{"id":"https://openalex.org/keywords/distance-matrix","display_name":"Distance matrix","score":0.4524681270122528},{"id":"https://openalex.org/keywords/lexicographical-order","display_name":"Lexicographical order","score":0.4374573528766632},{"id":"https://openalex.org/keywords/algebraic-connectivity","display_name":"Algebraic connectivity","score":0.42649421095848083},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3710656464099884},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3675879240036011},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20757481455802917},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2066928744316101},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.13637304306030273},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1290442943572998}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6494526863098145},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.6418872475624084},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.6274098753929138},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5624954700469971},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.5439822673797607},{"id":"https://openalex.org/C612898","wikidata":"https://www.wikidata.org/wiki/Q7315618","display_name":"Resistance distance","level":5,"score":0.5093070268630981},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4771163761615753},{"id":"https://openalex.org/C111208986","wikidata":"https://www.wikidata.org/wiki/Q901698","display_name":"Distance matrix","level":2,"score":0.4524681270122528},{"id":"https://openalex.org/C159254197","wikidata":"https://www.wikidata.org/wiki/Q1144915","display_name":"Lexicographical order","level":2,"score":0.4374573528766632},{"id":"https://openalex.org/C7948225","wikidata":"https://www.wikidata.org/wiki/Q4723998","display_name":"Algebraic connectivity","level":4,"score":0.42649421095848083},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3710656464099884},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3675879240036011},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20757481455802917},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2066928744316101},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.13637304306030273},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1290442943572998},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830920500615","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830920500615","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":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.7900000214576721}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1907302916","https://openalex.org/W1994300999","https://openalex.org/W2008194408","https://openalex.org/W2031324894","https://openalex.org/W2035666692","https://openalex.org/W2037357970","https://openalex.org/W2220507833","https://openalex.org/W2246567367","https://openalex.org/W2288664836","https://openalex.org/W2323784209","https://openalex.org/W2790264134","https://openalex.org/W2790688311","https://openalex.org/W2791326320","https://openalex.org/W2791818963","https://openalex.org/W2946375028","https://openalex.org/W2952260038","https://openalex.org/W4230572909"],"related_works":["https://openalex.org/W2031324894","https://openalex.org/W2286603664","https://openalex.org/W4200515925","https://openalex.org/W2792769346","https://openalex.org/W2081084405","https://openalex.org/W2280322458","https://openalex.org/W3135549895","https://openalex.org/W3021447162","https://openalex.org/W2066555486","https://openalex.org/W2954749020"],"abstract_inverted_index":{"For":[0],"a":[1],"simple":[2],"connected":[3,95,109],"graph":[4,122],"[Formula:":[5,10,17,24,30,34,42,57,101,114,119,142],"see":[6,11,18,25,31,35,43,58,102,115,120,143],"text]":[7,12,26,36,59,116],"of":[8,41,51,55,62,70,82,86,94,134],"order":[9],"having":[13],"distance":[14,21,48,64,79,91,126,135],"Laplacian":[15,22,49,65,80,92,127,136],"eigenvalues":[16,137],"text],":[19,32],"the":[20,38,47,52,68,78,83,90,117,124,132],"energy":[23,93],"is":[27,37],"defined":[28],"as":[29],"where":[33],"Wiener":[39],"index":[40],"text].":[44,103,144],"We":[45,88,104],"obtain":[46,77],"spectrum":[50,66,69,81],"joined":[53],"union":[54],"graphs":[56,96,110],"in":[60],"terms":[61],"their":[63],"and":[67],"an":[71],"auxiliary":[72],"matrix.":[73],"As":[74],"application,":[75],"we":[76,130],"lexicographic":[84],"product":[85],"graphs.":[87],"study":[89],"with":[97,111],"given":[98],"chromatic":[99,112],"number":[100,113],"show":[105],"that":[106],"among":[107],"all":[108],"complete":[118],"text]-partite":[121],"has":[123],"minimum":[125],"energy.":[128],"Further,":[129],"discuss":[131],"distribution":[133],"around":[138],"average":[139],"transmission":[140],"degree":[141]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}