{"id":"https://openalex.org/W3015867196","doi":"https://doi.org/10.1002/net.21938","title":"Rational roots of all\u2010terminal reliability","display_name":"Rational roots of all\u2010terminal reliability","publication_year":2020,"publication_date":"2020-04-09","ids":{"openalex":"https://openalex.org/W3015867196","doi":"https://doi.org/10.1002/net.21938","mag":"3015867196"},"language":"en","primary_location":{"id":"doi:10.1002/net.21938","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.21938","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"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":"Networks","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/A5045473830","display_name":"Jason I. Brown","orcid":"https://orcid.org/0000-0002-4721-8985"},"institutions":[{"id":"https://openalex.org/I129902397","display_name":"Dalhousie University","ror":"https://ror.org/01e6qks80","country_code":"CA","type":"education","lineage":["https://openalex.org/I129902397"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Jason I. Brown","raw_affiliation_strings":["Department of Mathematics and Statistics Dalhousie University  Halifax Nova Scotia Canada","Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada"],"raw_orcid":"https://orcid.org/0000-0002-4721-8985","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics Dalhousie University  Halifax Nova Scotia Canada","institution_ids":["https://openalex.org/I129902397"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada","institution_ids":["https://openalex.org/I129902397"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089420269","display_name":"Corey D. C. DeGagn\u00e9","orcid":null},"institutions":[{"id":"https://openalex.org/I129902397","display_name":"Dalhousie University","ror":"https://ror.org/01e6qks80","country_code":"CA","type":"education","lineage":["https://openalex.org/I129902397"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Corey D. C. DeGagn\u00e9","raw_affiliation_strings":["Department of Mathematics and Statistics Dalhousie University  Halifax Nova Scotia Canada","Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics Dalhousie University  Halifax Nova Scotia Canada","institution_ids":["https://openalex.org/I129902397"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada","institution_ids":["https://openalex.org/I129902397"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5045473830"],"corresponding_institution_ids":["https://openalex.org/I129902397"],"apc_list":{"value":3400,"currency":"USD","value_usd":3400},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.04266052,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"76","issue":"1","first_page":"75","last_page":"83"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10780","display_name":"Reliability and Maintenance Optimization","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2213","display_name":"Safety, Risk, Reliability and Quality"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10780","display_name":"Reliability and Maintenance Optimization","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/2213","display_name":"Safety, Risk, Reliability and Quality"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9861999750137329,"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/T10211","display_name":"Computational Drug Discovery Methods","score":0.9286999702453613,"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":0.7315735220909119},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6628344058990479},{"id":"https://openalex.org/keywords/terminal","display_name":"Terminal (telecommunication)","score":0.5337582230567932},{"id":"https://openalex.org/keywords/spanning-tree","display_name":"Spanning tree","score":0.5161693692207336},{"id":"https://openalex.org/keywords/rational-number","display_name":"Rational number","score":0.49898624420166016},{"id":"https://openalex.org/keywords/moduli","display_name":"Moduli","score":0.4876305162906647},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4722544550895691},{"id":"https://openalex.org/keywords/reliability","display_name":"Reliability (semiconductor)","score":0.4712287187576294},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45023757219314575},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4350108504295349},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.43094632029533386},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13985690474510193}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7315735220909119},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6628344058990479},{"id":"https://openalex.org/C2779664074","wikidata":"https://www.wikidata.org/wiki/Q3518405","display_name":"Terminal (telecommunication)","level":2,"score":0.5337582230567932},{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.5161693692207336},{"id":"https://openalex.org/C46875033","wikidata":"https://www.wikidata.org/wiki/Q1244890","display_name":"Rational number","level":2,"score":0.49898624420166016},{"id":"https://openalex.org/C121089165","wikidata":"https://www.wikidata.org/wiki/Q6889796","display_name":"Moduli","level":2,"score":0.4876305162906647},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4722544550895691},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.4712287187576294},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45023757219314575},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4350108504295349},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.43094632029533386},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13985690474510193},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"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/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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/net.21938","is_oa":false,"landing_page_url":"https://doi.org/10.1002/net.21938","pdf_url":null,"source":{"id":"https://openalex.org/S191798613","display_name":"Networks","issn_l":"0028-3045","issn":["0028-3045","1097-0037"],"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":"Networks","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6749251387","display_name":null,"funder_award_id":"RGPIN-2018-05227","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W181961416","https://openalex.org/W1484040084","https://openalex.org/W1653500785","https://openalex.org/W1966785002","https://openalex.org/W1972833039","https://openalex.org/W1985431191","https://openalex.org/W2014091871","https://openalex.org/W2020744076","https://openalex.org/W2031110152","https://openalex.org/W2039700046","https://openalex.org/W2109939969","https://openalex.org/W2117889403","https://openalex.org/W2130787236","https://openalex.org/W2600202171","https://openalex.org/W3104211280","https://openalex.org/W3105684108","https://openalex.org/W4290859712"],"related_works":["https://openalex.org/W4288313061","https://openalex.org/W3211557223","https://openalex.org/W2007036916","https://openalex.org/W2120266540","https://openalex.org/W2952928706","https://openalex.org/W872563264","https://openalex.org/W4206528302","https://openalex.org/W2164087676","https://openalex.org/W4310690328","https://openalex.org/W4226465938"],"abstract_inverted_index":{"Abstract":[0],"Given":[1],"a":[2,42,49,82],"connected":[3],"graph":[4],"G":[5,30],"whose":[6,12],"vertices":[7],"are":[8,112],"perfectly":[9],"reliable":[10],"and":[11,147,154,179],"edges":[13,40],"each":[14],"fail":[15],"independently":[16],"with":[17,66,72],"probability":[18,33,46],"q":[19,52],"\u2208":[20],"[0,":[21],"1]":[22],",":[23,133],"the":[24,32,35,57,73,98,109,134,155,161,170],"(":[25],"all\u2010terminal":[26],")":[27],"reliability":[28,60,86],"of":[29,38,56,59,88,136,142,151,172,184],"is":[31,47,145],"that":[34,103,128,166,183],"resulting":[36],"subgraph":[37],"operational":[39],"contains":[41],"spanning":[43],"tree":[44],"(this":[45],"always":[48],"polynomial":[50],"in":[51,69,186],").":[53],"The":[54],"location":[55],"roots":[58,111,150],"polynomials":[61,87],"has":[62],"been":[63],"well":[64],"studied,":[65],"particular":[67],"interest":[68],"finding":[70],"those":[71,176],"largest":[74],"moduli.":[75],"In":[76],"this":[77],"paper,":[78],"we":[79,95,126,159],"will":[80],"discuss":[81],"related":[83],"problem\u2014among":[84],"all":[85,140,149],"graphs":[89,141,174,185],"on":[90],"n":[91,105,120,130,144],"vertices,":[92],"what":[93],"can":[94],"say":[96],"about":[97],"rational":[99,110],"roots?":[100],"We":[101],"prove":[102],"(for":[104],"\u2265":[106,131],"2":[107],"),":[108],"\u22121,":[113],"\u2212":[114,116,118,121],"1/2,":[115],"1/3,\u2026,":[117],"1/(":[119],"1),":[122],"1":[123],".":[124],"Moreover,":[125],"show":[127],"for":[129],"3":[132],"root":[135],"minimum":[137],"modulus":[138],"among":[139],"order":[143],"rational,":[146],"determine":[148],"smallest":[152],"moduli":[153],"corresponding":[156],"graphs.":[157],"Finally,":[158],"provide":[160],"first":[162],"nontrivial":[163],"mathematical":[164],"property":[165],"distinguishes,":[167],"via":[168],"reliability,":[169],"class":[171],"simple":[173],"(i.e.,":[175],"without":[177],"loops":[178],"multiple":[180],"edges)":[181],"from":[182],"general.":[187]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}