{"id":"https://openalex.org/W6888859682","doi":"https://doi.org/10.22108/toc.2024.140831.2156","title":"$G$-designs for the connected triangular bicyclic graphs with nine edges","display_name":"$G$-designs for the connected triangular bicyclic graphs with nine edges","publication_year":2024,"publication_date":"2024-11-01","ids":{"openalex":"https://openalex.org/W6888859682","doi":"https://doi.org/10.22108/toc.2024.140831.2156"},"language":"en","primary_location":{"id":"pmh:oai:doaj.org/article:1fa22a1f7eaf44dc8aea9c34b8fa7269","doi":"https://doi.org/10.22108/toc.2024.140831.2156","is_oa":false,"landing_page_url":"https://doaj.org/article/1fa22a1f7eaf44dc8aea9c34b8fa7269","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Transactions on Combinatorics, Vol 14, Iss 4, Pp 271-281 (2024)","raw_type":"article"},"volume":null,"type":"article","indexed_in":["doaj"],"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/A5090304865","display_name":"Bryan Freyberg","orcid":"https://orcid.org/0000-0001-8246-5896","observed_orcids":["https://orcid.org/0000-0001-8246-5896"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bryan Freyberg","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Dalibor Froncek","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dalibor Froncek","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Joel Jeffries","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Joel Jeffries","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5144191444","display_name":"Gretta Jensen","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gretta Jensen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5095688152","display_name":"Andrew Sailstad","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andrew Sailstad","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.26287075,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.7968999743461609,"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":0.7968999743461609,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.1080000028014183,"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/T10849","display_name":"Finite Group Theory Research","score":0.053700000047683716,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/graph-decomposition","display_name":"graph decomposition","score":0.7870000004768372},{"id":"https://openalex.org/keywords/complete-graph-decomposition","display_name":"complete graph decomposition","score":0.7509999871253967},{"id":"https://openalex.org/keywords/bicyclic-graphs","display_name":"bicyclic graphs","score":0.890999972820282},{"id":"https://openalex.org/keywords/graph-factorization","display_name":"graph factorization","score":0.5910000205039978},{"id":"https://openalex.org/keywords/existence-conditions","display_name":"existence conditions","score":0.4860000014305115},{"id":"https://openalex.org/keywords/congruence-conditions","display_name":"congruence conditions","score":0.5950000286102295}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7548999786376953},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5896999835968018},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5799000263214111},{"id":"https://openalex.org/C24961977","wikidata":"https://www.wikidata.org/wiki/Q225972","display_name":"Bicyclic molecule","level":2,"score":0.4837999939918518},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.41510000824928284},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.39100000262260437},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38519999384880066},{"id":"https://openalex.org/C193435613","wikidata":"https://www.wikidata.org/wiki/Q2997928","display_name":"Connected component","level":2,"score":0.3239000141620636},{"id":"https://openalex.org/C125080357","wikidata":"https://www.wikidata.org/wiki/Q45715","display_name":"Complete graph","level":3,"score":0.323199987411499},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.2694999873638153},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.25929999351501465}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:doaj.org/article:1fa22a1f7eaf44dc8aea9c34b8fa7269","doi":"https://doi.org/10.22108/toc.2024.140831.2156","is_oa":false,"landing_page_url":"https://doaj.org/article/1fa22a1f7eaf44dc8aea9c34b8fa7269","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Transactions on Combinatorics, Vol 14, Iss 4, Pp 271-281 (2024)","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"A":[0],"$G$-design":[1,35],"of":[2,8,16,36],"order":[3,37],"$n$":[4,38],"is":[5,23],"a":[6,24,34],"decomposition":[7],"the":[9],"complete":[10],"graph":[11,27],"$K_n$":[12],"into":[13],"isomorphic":[14],"copies":[15],"$G$.":[17],"We":[18],"show":[19],"that":[20],"if":[21],"$G$":[22],"connected":[25],"bicyclic":[26],"with":[28],"nine":[29],"edges":[30],"containing":[31],"two":[32],"triangles,":[33],"exists":[39],"whenever":[40],"$n":[41],"\\equiv":[42],"0,1":[43],"\\pmod{18}$.":[44]},"counts_by_year":[],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2025-10-10T00:00:00"}
