{"title":"在有限群上，所有有界价的双凯利图都是积分的","authors":"M. Arezoomand","doi":"10.22108/TOC.2021.126275.1787","DOIUrl":null,"url":null,"abstract":"Let $kgeq 1$ be an integer and $mathcal{I}_k$ be the set of all finite groups $G$ such that every bi-Cayley graph $BCay(G,S)$ of $G$ with respect to subset $S$ of length $1leq |S|leq k$ is integral. Let $kgeq 3$. We prove that a finite group $G$ belongs to $mathcal{I}_k$ if and only if $GcongBbb Z_3$, $Bbb Z_2^r$ for some integer $r$, or $S_3$.","PeriodicalId":43837,"journal":{"name":"Transactions on Combinatorics","volume":"10 1","pages":"247-252"},"PeriodicalIF":0.6000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On finite groups all of whose bi-Cayley graphs of bounded valency are integral\",\"authors\":\"M. Arezoomand\",\"doi\":\"10.22108/TOC.2021.126275.1787\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $kgeq 1$ be an integer and $mathcal{I}_k$ be the set of all finite groups $G$ such that every bi-Cayley graph $BCay(G,S)$ of $G$ with respect to subset $S$ of length $1leq |S|leq k$ is integral. Let $kgeq 3$. We prove that a finite group $G$ belongs to $mathcal{I}_k$ if and only if $GcongBbb Z_3$, $Bbb Z_2^r$ for some integer $r$, or $S_3$.\",\"PeriodicalId\":43837,\"journal\":{\"name\":\"Transactions on Combinatorics\",\"volume\":\"10 1\",\"pages\":\"247-252\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions on Combinatorics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22108/TOC.2021.126275.1787\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions on Combinatorics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22108/TOC.2021.126275.1787","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
On finite groups all of whose bi-Cayley graphs of bounded valency are integral
Let $kgeq 1$ be an integer and $mathcal{I}_k$ be the set of all finite groups $G$ such that every bi-Cayley graph $BCay(G,S)$ of $G$ with respect to subset $S$ of length $1leq |S|leq k$ is integral. Let $kgeq 3$. We prove that a finite group $G$ belongs to $mathcal{I}_k$ if and only if $GcongBbb Z_3$, $Bbb Z_2^r$ for some integer $r$, or $S_3$.
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