{"title":"完美单元 Cayley 图的完整分类","authors":"Ján Mináč, Tung T. Nguyen, Nguyen Duy Tân","doi":"arxiv-2409.01922","DOIUrl":null,"url":null,"abstract":"Due to their elegant and simple nature, unitary Cayley graphs have been an\nactive research topic in the literature. These graphs are naturally connected\nto several branches of mathematics, including number theory, finite algebra,\nrepresentation theory, and graph theory. In this article, we study the\nperfectness property of these graphs. More precisely, we provide a complete\nclassification of perfect unitary Cayley graphs associated with finite rings.","PeriodicalId":501136,"journal":{"name":"arXiv - MATH - Rings and Algebras","volume":"49 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A complete classification of perfect unitary Cayley graphs\",\"authors\":\"Ján Mináč, Tung T. Nguyen, Nguyen Duy Tân\",\"doi\":\"arxiv-2409.01922\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Due to their elegant and simple nature, unitary Cayley graphs have been an\\nactive research topic in the literature. These graphs are naturally connected\\nto several branches of mathematics, including number theory, finite algebra,\\nrepresentation theory, and graph theory. In this article, we study the\\nperfectness property of these graphs. More precisely, we provide a complete\\nclassification of perfect unitary Cayley graphs associated with finite rings.\",\"PeriodicalId\":501136,\"journal\":{\"name\":\"arXiv - MATH - Rings and Algebras\",\"volume\":\"49 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Rings and Algebras\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.01922\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Rings and Algebras","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.01922","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A complete classification of perfect unitary Cayley graphs
Due to their elegant and simple nature, unitary Cayley graphs have been an
active research topic in the literature. These graphs are naturally connected
to several branches of mathematics, including number theory, finite algebra,
representation theory, and graph theory. In this article, we study the
perfectness property of these graphs. More precisely, we provide a complete
classification of perfect unitary Cayley graphs associated with finite rings.
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