{"id":"https://openalex.org/W2165035860","doi":"https://doi.org/10.1002/jgt.3190140309","title":"The distance spectrum of a tree","display_name":"The distance spectrum of a tree","publication_year":1990,"publication_date":"1990-07-01","ids":{"openalex":"https://openalex.org/W2165035860","doi":"https://doi.org/10.1002/jgt.3190140309","mag":"2165035860"},"language":"en","primary_location":{"id":"doi:10.1002/jgt.3190140309","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.3190140309","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","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/A5075558471","display_name":"Russell Merris","orcid":null},"institutions":[{"id":"https://openalex.org/I127339247","display_name":"California State University System","ror":"https://ror.org/020qm1538","country_code":"US","type":"education","lineage":["https://openalex.org/I127339247"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Russell Merris","raw_affiliation_strings":["Department of Mathematics, And Computer Science, California State University, Hayward, California"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, And Computer Science, California State University, Hayward, California","institution_ids":["https://openalex.org/I127339247"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5075558471"],"corresponding_institution_ids":["https://openalex.org/I127339247"],"apc_list":{"value":4150,"currency":"USD","value_usd":4150},"apc_paid":null,"fwci":2.1807,"has_fulltext":false,"cited_by_count":107,"citation_normalized_percentile":{"value":0.90307503,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"14","issue":"3","first_page":"365","last_page":"369"},"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9919000267982483,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9836000204086304,"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/mathematics","display_name":"Mathematics","score":0.8203911781311035},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7880228161811829},{"id":"https://openalex.org/keywords/adjacency-matrix","display_name":"Adjacency matrix","score":0.7780808806419373},{"id":"https://openalex.org/keywords/distance-matrix","display_name":"Distance matrix","score":0.753938615322113},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7088079452514648},{"id":"https://openalex.org/keywords/spectrum","display_name":"Spectrum (functional analysis)","score":0.6639289855957031},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.5667996406555176},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5033754706382751},{"id":"https://openalex.org/keywords/distance-matrices-in-phylogeny","display_name":"Distance matrices in phylogeny","score":0.4902406334877014},{"id":"https://openalex.org/keywords/adjacency-list","display_name":"Adjacency list","score":0.460128515958786},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4362652599811554},{"id":"https://openalex.org/keywords/spectrum-of-a-matrix","display_name":"Spectrum of a matrix","score":0.4267345070838928},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.41389259696006775},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36593762040138245},{"id":"https://openalex.org/keywords/matrix-differential-equation","display_name":"Matrix differential equation","score":0.0842774510383606},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06875964999198914},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.05644097924232483},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.055568546056747437}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8203911781311035},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7880228161811829},{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.7780808806419373},{"id":"https://openalex.org/C111208986","wikidata":"https://www.wikidata.org/wiki/Q901698","display_name":"Distance matrix","level":2,"score":0.753938615322113},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7088079452514648},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.6639289855957031},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5667996406555176},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5033754706382751},{"id":"https://openalex.org/C5349765","wikidata":"https://www.wikidata.org/wiki/Q5282866","display_name":"Distance matrices in phylogeny","level":2,"score":0.4902406334877014},{"id":"https://openalex.org/C110484373","wikidata":"https://www.wikidata.org/wiki/Q264398","display_name":"Adjacency list","level":2,"score":0.460128515958786},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4362652599811554},{"id":"https://openalex.org/C28940832","wikidata":"https://www.wikidata.org/wiki/Q3490774","display_name":"Spectrum of a matrix","level":4,"score":0.4267345070838928},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.41389259696006775},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36593762040138245},{"id":"https://openalex.org/C105671362","wikidata":"https://www.wikidata.org/wiki/Q6787870","display_name":"Matrix differential equation","level":3,"score":0.0842774510383606},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06875964999198914},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.05644097924232483},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.055568546056747437},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/jgt.3190140309","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.3190140309","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","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":22,"referenced_works":["https://openalex.org/W1528970839","https://openalex.org/W1560594658","https://openalex.org/W1587744656","https://openalex.org/W1597346751","https://openalex.org/W1964853142","https://openalex.org/W1977317053","https://openalex.org/W1984732727","https://openalex.org/W1994030344","https://openalex.org/W1996414791","https://openalex.org/W2001811808","https://openalex.org/W2040603850","https://openalex.org/W2047018652","https://openalex.org/W2048159843","https://openalex.org/W2067602704","https://openalex.org/W2076896360","https://openalex.org/W2116451290","https://openalex.org/W2151417892","https://openalex.org/W2335911270","https://openalex.org/W2724012211","https://openalex.org/W2785506964","https://openalex.org/W4249367555","https://openalex.org/W6702684557"],"related_works":["https://openalex.org/W4213150077","https://openalex.org/W2001076853","https://openalex.org/W1872375678","https://openalex.org/W2369410163","https://openalex.org/W2078477160","https://openalex.org/W2982430984","https://openalex.org/W1974398340","https://openalex.org/W2737156094","https://openalex.org/W2189347543","https://openalex.org/W4389420649"],"abstract_inverted_index":{"Abstract":[0],"Let":[1],"T":[2],"be":[3,45],"a":[4],"tree":[5],"with":[6],"line":[7],"graph":[8],"T*.":[9],"Define":[10],"K":[11,43],"=":[12],"2I":[13],"+":[14],"A(T*),":[15],"where":[16],"A":[17],"denotes":[18],"the":[19,23,28,31,40,48],"adjacency":[20],"matrix.":[21],"Then":[22],"eigenvalues":[24,29],"of":[25,30,42],"\u20102K\u22121":[26],"interlace":[27],"distance":[32],"matrix":[33],"D.":[34,51],"This":[35],"permits":[36],"numerous":[37],"results":[38],"about":[39],"spectrum":[41],"to":[44],"transcribed":[46],"for":[47],"less":[49],"tractable":[50]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":12},{"year":2012,"cited_by_count":15}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}