{"id":"https://openalex.org/W4413624477","doi":"https://doi.org/10.1007/s10623-025-01721-w","title":"Exact values and improved bounds on the clique number of cyclotomic graphs","display_name":"Exact values and improved bounds on the clique number of cyclotomic graphs","publication_year":2025,"publication_date":"2025-08-26","ids":{"openalex":"https://openalex.org/W4413624477","doi":"https://doi.org/10.1007/s10623-025-01721-w"},"language":"en","primary_location":{"id":"doi:10.1007/s10623-025-01721-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-025-01721-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-025-01721-w.pdf","source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10623-025-01721-w.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061055178","display_name":"Chi Hoi Yip","orcid":"https://orcid.org/0000-0003-0753-1675"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Chi Hoi Yip","raw_affiliation_strings":["School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332, USA","institution_ids":["https://openalex.org/I130701444"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5061055178"],"corresponding_institution_ids":["https://openalex.org/I130701444"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":8.6433,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.97779519,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"93","issue":"12","first_page":"5131","last_page":"5142"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9998999834060669,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9998999834060669,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9998000264167786,"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":0.9997000098228455,"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/mathematics","display_name":"Mathematics","score":0.9274110794067383},{"id":"https://openalex.org/keywords/clique","display_name":"Clique","score":0.7552777528762817},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6360548734664917},{"id":"https://openalex.org/keywords/clique-number","display_name":"Clique number","score":0.6174238920211792},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4601131081581116},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.23056766390800476}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9274110794067383},{"id":"https://openalex.org/C2777035058","wikidata":"https://www.wikidata.org/wiki/Q1662634","display_name":"Clique","level":2,"score":0.7552777528762817},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6360548734664917},{"id":"https://openalex.org/C2985491264","wikidata":"https://www.wikidata.org/wiki/Q761631","display_name":"Clique number","level":3,"score":0.6174238920211792},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4601131081581116},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.23056766390800476}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10623-025-01721-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-025-01721-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-025-01721-w.pdf","source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10623-025-01721-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-025-01721-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-025-01721-w.pdf","source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4413624477.pdf","grobid_xml":"https://content.openalex.org/works/W4413624477.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W186143519","https://openalex.org/W820979427","https://openalex.org/W1966750408","https://openalex.org/W1992036267","https://openalex.org/W2030239329","https://openalex.org/W2042472269","https://openalex.org/W2150052232","https://openalex.org/W2166882067","https://openalex.org/W2586639504","https://openalex.org/W3011473838","https://openalex.org/W3014751857","https://openalex.org/W3015106125","https://openalex.org/W3098671591","https://openalex.org/W3135556622","https://openalex.org/W3206433089","https://openalex.org/W3215154115","https://openalex.org/W4206279103","https://openalex.org/W4224028657","https://openalex.org/W4230136249","https://openalex.org/W4386254087"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1985876622","https://openalex.org/W4368364082","https://openalex.org/W1917172320","https://openalex.org/W2079729497","https://openalex.org/W4210610621","https://openalex.org/W2923758900","https://openalex.org/W2910420185","https://openalex.org/W2952711994","https://openalex.org/W4298162383"],"abstract_inverted_index":{"Abstract":[0],"Let":[1],"q":[2,232],"be":[3,204],"an":[4,181],"odd":[5],"power":[6],"of":[7,67,131,158,163,169,184,217],"a":[8,136,210,221],"prime":[9],"p":[10],",":[11,115],"and":[12,41,144,171,188],"$$S":[13],"\\subseteq":[14],"\\mathbb":[15,44],"{F}_q^*$$":[16,45],"<mml:math":[17,32,46,74,93,120],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[18,33,47,75,94,121],"<mml:mrow>":[19,34,48,76,95,97,107],"<mml:mi>S</mml:mi>":[20,35,38,49,51,85,99,101],"<mml:mo>\u2286</mml:mo>":[21],"<mml:msubsup>":[22,53,79],"<mml:mi>F</mml:mi>":[23,54,80],"<mml:mi>q</mml:mi>":[24,55,81,108,123],"<mml:mo>\u2217</mml:mo>":[25,56],"</mml:msubsup>":[26,57,83],"</mml:mrow>":[27,39,58,87,103,111,113],"</mml:math>":[28,40,59,88,114,125],"such":[29,132],"that":[30,63],"$$S=-S$$":[31],"<mml:mo>=</mml:mo>":[36],"<mml:mo>-</mml:mo>":[37],"$$S/S":[42],"\\ne":[43],"<mml:mo>/</mml:mo>":[50,100,109],"<mml:mo>\u2260</mml:mo>":[52],".":[60],"We":[61,207],"show":[62],"the":[64,68,117,149,155,167,192,200,215,226],"clique":[65,156,201],"number":[66,157,202,216],"Cayley":[69],"graph":[70],"$$\\operatorname":[71],"{Cay}(\\mathbb":[72],"{F}_q^+,S)$$":[73],"<mml:mo>Cay</mml:mo>":[77],"<mml:mo>(</mml:mo>":[78],"<mml:mo>+</mml:mo>":[82,105],"<mml:mo>,</mml:mo>":[84],"<mml:mo>)</mml:mo>":[86],"is":[89,139,177,235],"at":[90],"most":[91],"$$\\sqrt{|S/S|}+\\sqrt{q/p}$$":[92],"<mml:msqrt>":[96,106,122],"<mml:mo>|</mml:mo>":[98,102],"</mml:msqrt>":[104,112,124],"<mml:mi>p</mml:mi>":[110],"improving":[116],"best-known":[118],"$$\\sqrt{q}$$":[119],"upper":[126,152],"bound":[127,138,153,176,213],"for":[128,141,180,198,237],"many":[129],"families":[130],"graphs":[133,143,162],"substantially.":[134],"Such":[135],"new":[137,175,211],"strongest":[140],"cyclotomic":[142],"in":[145,225],"particular,":[146],"it":[147],"implies":[148],"first":[150,193],"nontrivial":[151,194],"on":[154,214],"all":[159],"generalized":[160,185],"Paley":[161,186],"non-square":[164],"order,":[165],"extending":[166],"work":[168],"Hanson":[170],"Petridis.":[172],"Moreover,":[173],"our":[174],"asymptotically":[178],"sharp":[179,236],"infinite":[182,238],"family":[183,195],"graphs,":[187],"we":[189],"further":[190],"discover":[191],"among":[196],"them":[197],"which":[199,234],"can":[203],"exactly":[205],"determined.":[206],"also":[208],"obtain":[209],"lower":[212],"directions":[218],"determined":[219],"by":[220],"large":[222],"Cartesian":[223],"product":[224],"affine":[227],"Galois":[228],"plane":[229],"AG":[230],"(2,":[231],"),":[233],"families.":[239]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-06-13T06:13:01.061226","created_date":"2025-10-10T00:00:00"}