{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:40Z","timestamp":1753893820423,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>\r\nA Cayley digraph $\\mathrm{Cay}(G,S)$ of a finite group $G$ with respect to a subset $S$ of $G$ is said to be a CI-digraph if for every Cayley digraph $\\mathrm{Cay}(G,T)$ isomorphic to $\\mathrm{Cay}(G,S)$, there exists an automorphism $\\sigma$ of $G$ such that $S^\\sigma=T$. A finite group $G$ is said to have the $m$-DCI property for some positive integer $m$ if every Cayley digraph $\\mathrm{Cay}(G,S)$ of $G$ with $|S|=m$ is a CI-digraph, and is said to be a DCI-group if $G$ has the $m$-DCI property for all $1\\leq m\\leq |G|$. Let $\\mathrm{Q}_{4n}$ be a generalized quaternion group (also called dicyclic group) of order $4n$ with an integer $n\\geq 3$, and let $\\mathrm{Q}_{4n}$ have the $m$-DCI property for some $1 \\leq m\\leq 2n-1$. It is shown in this paper that $n$ is odd, and $n$ is not divisible by $p^2$ for any prime $p\\leq m-1$. Furthermore, if $n\\geq 3$ is a power of a prime $p$, then $\\mathrm{Q}_{4n}$ has the $m$-DCI property if and only if $p$ is odd, and either $n=p$ or $1\\leq m\\leq p$.\r\n<\/jats:p>","DOI":"10.37236\/12813","type":"journal-article","created":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T15:19:09Z","timestamp":1750346349000},"source":"Crossref","is-referenced-by-count":0,"title":["Generalized Quaternion Groups with the $m$-DCI Property"],"prefix":"10.37236","volume":"32","author":[{"given":"Jinhua","family":"Xie","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yan-Quan","family":"Feng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Binzhou","family":"Xia","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2025,6,20]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i2p47\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i2p47\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T15:19:09Z","timestamp":1750346349000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v32i2p47"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,20]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,4,11]]}},"URL":"https:\/\/doi.org\/10.37236\/12813","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2025,6,20]]},"article-number":"P2.47"}}