{"id":"https://openalex.org/W1537535468","doi":"https://doi.org/10.37236/3679","title":"Certificates for Properties of Stability Polynomials of Graphs","display_name":"Certificates for Properties of Stability Polynomials of Graphs","publication_year":2014,"publication_date":"2014-03-24","ids":{"openalex":"https://openalex.org/W1537535468","doi":"https://doi.org/10.37236/3679","mag":"1537535468"},"language":"en","primary_location":{"id":"doi:10.37236/3679","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3679","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v21i1p67/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/v21i1p67/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087476014","display_name":"Ranjie Mo","orcid":null},"institutions":[{"id":"https://openalex.org/I2801239119","display_name":"Australian Regenerative Medicine Institute","ror":"https://ror.org/02qa5kg76","country_code":"AU","type":"facility","lineage":["https://openalex.org/I2801037857","https://openalex.org/I2801239119","https://openalex.org/I56590836"]},{"id":"https://openalex.org/I56590836","display_name":"Monash University","ror":"https://ror.org/02bfwt286","country_code":"AU","type":"education","lineage":["https://openalex.org/I56590836"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Ranjie Mo","raw_affiliation_strings":["Monash University","Monash university"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Monash University","institution_ids":["https://openalex.org/I2801239119","https://openalex.org/I56590836"]},{"raw_affiliation_string":"Monash university","institution_ids":["https://openalex.org/I2801239119"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005637509","display_name":"Graham Farr","orcid":null},"institutions":[{"id":"https://openalex.org/I2801239119","display_name":"Australian Regenerative Medicine Institute","ror":"https://ror.org/02qa5kg76","country_code":"AU","type":"facility","lineage":["https://openalex.org/I2801037857","https://openalex.org/I2801239119","https://openalex.org/I56590836"]},{"id":"https://openalex.org/I56590836","display_name":"Monash University","ror":"https://ror.org/02bfwt286","country_code":"AU","type":"education","lineage":["https://openalex.org/I56590836"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Graham Farr","raw_affiliation_strings":["Monash University","Monash university"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Monash University","institution_ids":["https://openalex.org/I2801239119","https://openalex.org/I56590836"]},{"raw_affiliation_string":"Monash university","institution_ids":["https://openalex.org/I2801239119"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025441020","display_name":"Kerri Morgan","orcid":"https://orcid.org/0000-0002-7263-8340"},"institutions":[{"id":"https://openalex.org/I2801239119","display_name":"Australian Regenerative Medicine Institute","ror":"https://ror.org/02qa5kg76","country_code":"AU","type":"facility","lineage":["https://openalex.org/I2801037857","https://openalex.org/I2801239119","https://openalex.org/I56590836"]},{"id":"https://openalex.org/I56590836","display_name":"Monash University","ror":"https://ror.org/02bfwt286","country_code":"AU","type":"education","lineage":["https://openalex.org/I56590836"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Kerri Morgan","raw_affiliation_strings":["Monash University","Monash university"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Monash University","institution_ids":["https://openalex.org/I2801239119","https://openalex.org/I56590836"]},{"raw_affiliation_string":"Monash university","institution_ids":["https://openalex.org/I2801239119"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3574,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.59458903,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"21","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9894000291824341,"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"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9894000291824341,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9771000146865845,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9607999920845032,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.828778862953186},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8002403974533081},{"id":"https://openalex.org/keywords/chromatic-polynomial","display_name":"Chromatic polynomial","score":0.7352092862129211},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.6825689673423767},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5828222036361694},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.5325364470481873},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4844217598438263},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.47428470849990845},{"id":"https://openalex.org/keywords/independent-set","display_name":"Independent set","score":0.45230984687805176},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3973580002784729}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.828778862953186},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8002403974533081},{"id":"https://openalex.org/C126385604","wikidata":"https://www.wikidata.org/wiki/Q1087609","display_name":"Chromatic polynomial","level":3,"score":0.7352092862129211},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.6825689673423767},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5828222036361694},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.5325364470481873},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4844217598438263},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.47428470849990845},{"id":"https://openalex.org/C122818955","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independent set","level":3,"score":0.45230984687805176},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3973580002784729},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/3679","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3679","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v21i1p67/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"},{"id":"pmh:oai:dro.deakin.edu.au:DU:30107605","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306402457","display_name":"Deakin Research Online (Deakin University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149704539","host_organization_name":"Deakin University","host_organization_lineage":["https://openalex.org/I149704539"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},{"id":"pmh:oai:figshare.com:article/20812060","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Certificates_for_properties_of_stability_polynomials_of_graphs/20812060","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"}],"best_oa_location":{"id":"doi:10.37236/3679","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3679","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v21i1p67/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/G4422861127","display_name":"An algebraic renaissance for the chromatic polynomial","funder_award_id":"DP110100957","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"}],"funders":[{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1537535468.pdf","grobid_xml":"https://content.openalex.org/works/W1537535468.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W206605580","https://openalex.org/W1536180355","https://openalex.org/W1583289006","https://openalex.org/W1831506627","https://openalex.org/W1969007797","https://openalex.org/W1979786782","https://openalex.org/W1982992685","https://openalex.org/W2082338474","https://openalex.org/W2319873605","https://openalex.org/W2937380089","https://openalex.org/W4205898702","https://openalex.org/W6762051492"],"related_works":["https://openalex.org/W1971174658","https://openalex.org/W2099195351","https://openalex.org/W4256429076","https://openalex.org/W2012063272","https://openalex.org/W2348092930","https://openalex.org/W2356950793","https://openalex.org/W2138685729","https://openalex.org/W2017638499","https://openalex.org/W4297803065","https://openalex.org/W2886071965"],"abstract_inverted_index":{"A":[0],"stable":[1,41],"(or":[2],"independent)":[3],"set":[4,7,18,35],"is":[5,30,40,50,57,90,112,132],"a":[6,27,34,64,113],"of":[8,13,26,36,45,71,82,116,139,142,154,161,164,170,173,185,188,211,218],"vertices":[9,15,39],"where":[10,42,125],"no":[11],"two":[12,148,201,215],"the":[14,17,31,43,60,83,162,183,186,204],"in":[16,63,159],"are":[19,178,190],"adjacent.":[20],"The":[21,86],"stability":[22,72,87,198,206,212],"polynomial":[23,56,62,88],"$A(G;":[24,102],"p)$":[25],"graph":[28],"$G$":[29,111,131],"probability":[32,44],"that":[33],"randomly":[37],"chosen":[38,49],"each":[46],"vertex":[47],"being":[48],"$p$,":[51],"with":[52,96],"choices":[53],"independent.":[54],"This":[55,67,107],"analogous":[58],"to":[59,92,156,196],"chromatic":[61,84],"precise":[65],"sense.":[66],"paper":[68],"considers":[69],"factorisation":[70,81,127],"polynomials,":[73],"following":[74],"work":[75],"by":[76],"Morgan":[77],"and":[78,99,118,147],"Farr":[79],"on":[80],"polynomial.":[85,207],"$A(G;p)$":[89],"said":[91],"have":[93,203],"an":[94],"s-factorisation":[95,155],"s-factors":[97],"$H_{1}$":[98,117],"$H_{2}$":[100],"if":[101],"p)":[103],"=":[104],"A(H_{1};p)":[105],"A(H_{2};p)$.":[106],"clearly":[108],"occurs":[109,128],"when":[110,130,200],"disjoint":[114],"union":[115],"$H_{2}$.":[119],"We":[120,134,151,192,208],"find":[121,135],"many":[122],"other":[123],"cases":[124],"such":[126],"even":[129],"connected.":[133],"152":[136],"different":[137],"s-factorisations":[138,158,169,189],"connected":[140,171],"graphs":[141,172,202],"order":[143,174],"at":[144,175],"most":[145,176],"9,":[146],"infinite":[149,216],"families.":[150],"introduce":[152],"certificates":[153,167,187,195],"explain":[157,197],"terms":[160],"structure":[163],"$G$.":[165],"Short":[166],"for":[168,182,214],"6":[177],"found.":[179],"Upper":[180],"bounds":[181],"lengths":[184],"given.":[191],"also":[193],"use":[194],"equivalence,":[199],"same":[205],"give":[209],"certifications":[210],"equivalence":[213],"families":[217],"graphs.":[219]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
