{"id":"https://openalex.org/W4400589110","doi":"https://doi.org/10.37236/12850","title":"Note on the Spectra of Steiner Distance Hypermatrices","display_name":"Note on the Spectra of Steiner Distance Hypermatrices","publication_year":2024,"publication_date":"2024-07-12","ids":{"openalex":"https://openalex.org/W4400589110","doi":"https://doi.org/10.37236/12850"},"language":"en","primary_location":{"id":"doi:10.37236/12850","is_oa":true,"landing_page_url":"https://doi.org/10.37236/12850","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v31i3p4/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/v31i3p4/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001619842","display_name":"Joshua Cooper","orcid":"https://orcid.org/0000-0001-5187-1322"},"institutions":[{"id":"https://openalex.org/I155781252","display_name":"University of South Carolina","ror":"https://ror.org/02b6qw903","country_code":"US","type":"education","lineage":["https://openalex.org/I155781252"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Joshua Cooper","raw_affiliation_strings":["University of South Carolina"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of South Carolina","institution_ids":["https://openalex.org/I155781252"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004929939","display_name":"Zhibin Du","orcid":"https://orcid.org/0000-0001-5795-3580"},"institutions":[{"id":"https://openalex.org/I187400657","display_name":"South China Normal University","ror":"https://ror.org/01kq0pv72","country_code":"CN","type":"education","lineage":["https://openalex.org/I187400657"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhibin Du","raw_affiliation_strings":["South China Normal University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"South China Normal University","institution_ids":["https://openalex.org/I187400657"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9335,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.7125323,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"31","issue":"3","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":0.9708999991416931,"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":0.9708999991416931,"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/T10621","display_name":"Gene Regulatory Network Analysis","score":0.944599986076355,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10540","display_name":"Advanced Fluorescence Microscopy Techniques","score":0.9316999912261963,"subfield":{"id":"https://openalex.org/subfields/1304","display_name":"Biophysics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8806900978088379},{"id":"https://openalex.org/keywords/distance-matrix","display_name":"Distance matrix","score":0.757671594619751},{"id":"https://openalex.org/keywords/steiner-tree-problem","display_name":"Steiner tree problem","score":0.7542682886123657},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7328936457633972},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6193237900733948},{"id":"https://openalex.org/keywords/spectral-radius","display_name":"Spectral radius","score":0.5762108564376831},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5338472127914429},{"id":"https://openalex.org/keywords/connectivity","display_name":"Connectivity","score":0.49895596504211426},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.44919300079345703},{"id":"https://openalex.org/keywords/vertex-connectivity","display_name":"Vertex connectivity","score":0.42047548294067383},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37315213680267334},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.17922508716583252},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11569914221763611}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8806900978088379},{"id":"https://openalex.org/C111208986","wikidata":"https://www.wikidata.org/wiki/Q901698","display_name":"Distance matrix","level":2,"score":0.757671594619751},{"id":"https://openalex.org/C76220878","wikidata":"https://www.wikidata.org/wiki/Q1764144","display_name":"Steiner tree problem","level":2,"score":0.7542682886123657},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7328936457633972},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6193237900733948},{"id":"https://openalex.org/C140532419","wikidata":"https://www.wikidata.org/wiki/Q249748","display_name":"Spectral radius","level":3,"score":0.5762108564376831},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5338472127914429},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.49895596504211426},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.44919300079345703},{"id":"https://openalex.org/C2983226441","wikidata":"https://www.wikidata.org/wiki/Q3115621","display_name":"Vertex connectivity","level":4,"score":0.42047548294067383},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37315213680267334},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.17922508716583252},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11569914221763611},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/12850","is_oa":true,"landing_page_url":"https://doi.org/10.37236/12850","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v31i3p4/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/12850","is_oa":true,"landing_page_url":"https://doi.org/10.37236/12850","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v31i3p4/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/G1416029241","display_name":null,"funder_award_id":"2023A1515011472","funder_id":"https://openalex.org/F4320337111","funder_display_name":"Basic and Applied Basic Research Foundation of Guangdong Province"}],"funders":[{"id":"https://openalex.org/F4320337111","display_name":"Basic and Applied Basic Research Foundation of Guangdong Province","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4400589110.pdf","grobid_xml":"https://content.openalex.org/works/W4400589110.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2963609423","https://openalex.org/W3166728817","https://openalex.org/W1803810968","https://openalex.org/W2771387978","https://openalex.org/W2080519708","https://openalex.org/W3092573672","https://openalex.org/W4296679228","https://openalex.org/W4306793219","https://openalex.org/W2472610420","https://openalex.org/W4283838100"],"abstract_inverted_index":{"The":[0,24],"Steiner":[1,26,50,103],"distance":[2,27,66,82,104,158],"of":[3,6,15,29,52,59,68,80,84,93,101,106,136],"a":[4,9,69,85,107],"set":[5],"vertices":[7],"in":[8,17,75],"graph":[10,32],"is":[11,33,120,163],"the":[12,34,49,57,64,78,81,99,102,137,141,151,157],"fewest":[13],"number":[14,91],"edges":[16],"any":[18],"connected":[19],"subgraph":[20],"containing":[21],"those":[22],"vertices.":[23,94],"order-$k$":[25],"hypermatrix":[28,105],"an":[30],"$n$-vertex":[31],"$n":[35,115],"\\times":[36,38],"\\cdots":[37],"n$":[39],"($k$":[40],"terms)":[41],"array":[42],"indexed":[43],"by":[44],"vertices,":[45],"whose":[46],"entries":[47],"are":[48,134,171],"distances":[51],"their":[53],"corresponding":[54],"indices.":[55],"In":[56],"case":[58,139],"$k=2$,":[60],"this":[61],"reduces":[62],"to":[63,154,165],"classical":[65],"matrix":[67,83],"graph.":[70],"Graham":[71],"and":[72,111,118,127,148],"Pollak":[73],"showed":[74],"1971":[76],"that":[77,98,156],"determinant":[79],"tree":[86,108],"only":[87,112],"depends":[88],"on":[89],"its":[90],"$n$":[92],"Here,":[95],"we":[96,149],"show":[97,155],"hyperdeterminant":[100],"vanishes":[109],"if":[110,113],"(a)":[114],"\\geq":[116],"3$":[117],"$k$":[119],"odd,":[121],"(b)":[122],"$n=1$,":[123],"or":[124],"(c)":[125],"$n=2$":[126,138,162],"$k":[128],"\\equiv":[129],"1":[130],"\\pmod{6}$.":[131],"Two":[132],"proofs":[133],"presented":[135],"-":[140,147],"other":[142],"situations":[143],"were":[144],"handled":[145],"previously":[146],"use":[150],"argument":[152],"further":[153],"spectral":[159],"radius":[160],"for":[161],"equal":[164],"$2^{k-1}-1$.":[166],"Some":[167],"related":[168],"open":[169],"questions":[170],"also":[172],"discussed.":[173]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
