{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,27]],"date-time":"2025-09-27T08:25:28Z","timestamp":1758961528727,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>An undirected graph is called integral, if all of its eigenvalues are integers.  Let $\\Gamma =Z_{m_1}\\otimes \\ldots \\otimes Z_{m_r}$ be an abelian group represented as the direct product of cyclic groups $Z_{m_i}$ of order $m_i$ such that all greatest common divisors $\\gcd(m_i,m_j)\\leq 2$ for $i\\neq j$. We prove that a Cayley graph $Cay(\\Gamma,S)$ over $\\Gamma$ is integral, if and only if $S\\subseteq \\Gamma$ belongs to the the Boolean algebra $B(\\Gamma)$ generated by the subgroups of $\\Gamma$.  It is also shown that every $S\\in B(\\Gamma)$ can be characterized by greatest common divisors.<\/jats:p>","DOI":"10.37236\/581","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:48:18Z","timestamp":1578714498000},"source":"Crossref","is-referenced-by-count":8,"title":["Integral Cayley Graphs Defined by Greatest Common Divisors"],"prefix":"10.37236","volume":"18","author":[{"given":"Walter","family":"Klotz","sequence":"first","affiliation":[]},{"given":"Torsten","family":"Sander","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2011,4,21]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p94\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p94\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:12:59Z","timestamp":1579302779000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p94"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,4,21]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/581","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,4,21]]},"article-number":"P94"}}