{"id":"https://openalex.org/W1787294921","doi":"https://doi.org/10.37236/350","title":"A Conjecture of Biggs Concerning the Resistance of a Distance-Regular Graph","display_name":"A Conjecture of Biggs Concerning the Resistance of a Distance-Regular Graph","publication_year":2010,"publication_date":"2010-05-25","ids":{"openalex":"https://openalex.org/W1787294921","doi":"https://doi.org/10.37236/350","mag":"1787294921"},"language":"en","primary_location":{"id":"doi:10.37236/350","is_oa":true,"landing_page_url":"https://doi.org/10.37236/350","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r78/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":null,"license_id":null,"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/v17i1r78/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086353857","display_name":"Greg Markowsky","orcid":"https://orcid.org/0000-0003-1656-337X"},"institutions":[{"id":"https://openalex.org/I123900574","display_name":"Pohang University of Science and Technology","ror":"https://ror.org/04xysgw12","country_code":"KR","type":"education","lineage":["https://openalex.org/I123900574"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Greg Markowsky","raw_affiliation_strings":["Pohang Mathematics Institute Department of Mathematics POSTECH POSTECH Pohang, 790-784 Pohang, 790-784 Republic of Korea Republic of Korea","Pohang University of Science and Technology"],"affiliations":[{"raw_affiliation_string":"Pohang Mathematics Institute Department of Mathematics POSTECH POSTECH Pohang, 790-784 Pohang, 790-784 Republic of Korea Republic of Korea","institution_ids":["https://openalex.org/I123900574"]},{"raw_affiliation_string":"Pohang University of Science and Technology","institution_ids":["https://openalex.org/I123900574"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048096758","display_name":"Jack H. Koolen","orcid":"https://orcid.org/0000-0002-8623-5681"},"institutions":[{"id":"https://openalex.org/I123900574","display_name":"Pohang University of Science and Technology","ror":"https://ror.org/04xysgw12","country_code":"KR","type":"education","lineage":["https://openalex.org/I123900574"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Jacobus Koolen","raw_affiliation_strings":["Pohang Mathematics Institute Department of Mathematics POSTECH POSTECH Pohang, 790-784 Pohang, 790-784 Republic of Korea Republic of Korea","Pohang University of Science and Technology"],"affiliations":[{"raw_affiliation_string":"Pohang Mathematics Institute Department of Mathematics POSTECH POSTECH Pohang, 790-784 Pohang, 790-784 Republic of Korea Republic of Korea","institution_ids":["https://openalex.org/I123900574"]},{"raw_affiliation_string":"Pohang University of Science and Technology","institution_ids":["https://openalex.org/I123900574"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5086353857"],"corresponding_institution_ids":["https://openalex.org/I123900574"],"apc_list":null,"apc_paid":null,"fwci":1.901,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.81021127,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"17","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9997000098228455,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9987999796867371,"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/T11476","display_name":"Graph theory and applications","score":0.9980999827384949,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.8725175261497498},{"id":"https://openalex.org/keywords/valency","display_name":"Valency","score":0.8628690838813782},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8503983020782471},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.664118766784668},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5722139477729797},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4647718071937561},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.42500314116477966},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39891719818115234},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06271910667419434},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.05617731809616089}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8725175261497498},{"id":"https://openalex.org/C139007053","wikidata":"https://www.wikidata.org/wiki/Q1412952","display_name":"Valency","level":2,"score":0.8628690838813782},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8503983020782471},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.664118766784668},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5722139477729797},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4647718071937561},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.42500314116477966},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39891719818115234},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06271910667419434},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.05617731809616089},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/350","is_oa":true,"landing_page_url":"https://doi.org/10.37236/350","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r78/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:oasis.postech.ac.kr:2014.oak/25571","is_oa":false,"landing_page_url":"https://oasis.postech.ac.kr/handle/2014.oak/25571","pdf_url":null,"source":{"id":"https://openalex.org/S4306401965","display_name":"Open Access System for Information Sharing (Pohang University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I123900574","host_organization_name":"Pohang University of Science and Technology","host_organization_lineage":["https://openalex.org/I123900574"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.37236/350","is_oa":true,"landing_page_url":"https://doi.org/10.37236/350","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r78/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.5099999904632568,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G1714819300","display_name":null,"funder_award_id":"2009-0089826","funder_id":"https://openalex.org/F4320322349","funder_display_name":"Ministry of Education, Science and Technology"},{"id":"https://openalex.org/G2988137300","display_name":null,"funder_award_id":"2009-0094070","funder_id":"https://openalex.org/F4320322349","funder_display_name":"Ministry of Education, Science and Technology"},{"id":"https://openalex.org/G342704958","display_name":null,"funder_award_id":"funded","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"}],"funders":[{"id":"https://openalex.org/F4320320671","display_name":"National Research Foundation","ror":"https://ror.org/05s0g1g46"},{"id":"https://openalex.org/F4320322120","display_name":"National Research Foundation of Korea","ror":"https://ror.org/013aysd81"},{"id":"https://openalex.org/F4320322349","display_name":"Ministry of Education, Science and Technology","ror":"https://ror.org/01p262204"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1787294921.pdf","grobid_xml":"https://content.openalex.org/works/W1787294921.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W118621918","https://openalex.org/W135807975","https://openalex.org/W1992908821","https://openalex.org/W2109842176","https://openalex.org/W2111293718","https://openalex.org/W2138033161","https://openalex.org/W2156644942","https://openalex.org/W2167064216","https://openalex.org/W2170807097","https://openalex.org/W2596139140","https://openalex.org/W4298236575","https://openalex.org/W6600618482","https://openalex.org/W6631337582","https://openalex.org/W6640929945"],"related_works":["https://openalex.org/W2762663192","https://openalex.org/W1992814711","https://openalex.org/W431658849","https://openalex.org/W1998523619","https://openalex.org/W638739646","https://openalex.org/W4212917371","https://openalex.org/W1979918629","https://openalex.org/W1974322723","https://openalex.org/W2043335234","https://openalex.org/W3210126571"],"abstract_inverted_index":{"Biggs":[0],"conjectured":[1],"that":[2],"the":[3,22,32,36,40,44],"resistance":[4,23],"between":[5,24],"any":[6],"two":[7],"points":[8],"on":[9],"a":[10],"distance-regular":[11],"graph":[12],"of":[13],"valency":[14],"greater":[15],"than":[16],"2":[17],"is":[18,53],"bounded":[19],"by":[20],"twice":[21],"adjacent":[25],"points.":[26],"We":[27],"prove":[28],"this":[29],"conjecture,":[30],"give":[31],"sharp":[33],"constant":[34],"for":[35,42],"inequality,":[37],"and":[38],"display":[39],"graphs":[41],"which":[43],"conjecture":[45],"most":[46],"nearly":[47],"fails.":[48],"Some":[49],"necessary":[50],"background":[51],"material":[52],"included,":[54],"as":[55,57],"well":[56],"some":[58],"consequences.":[59]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
