{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T15:23:57Z","timestamp":1769181837118,"version":"3.49.0"},"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>Let $\\Gamma$ be a finite, additive group, $S \\subseteq \\Gamma, 0\\notin S, -S=\\{-s: s\\in S\\}=S$.  The undirected Cayley graph Cay$(\\Gamma,S)$ has vertex set $\\Gamma$ and edge set $\\{\\{a,b\\}: a,b\\in \\Gamma$, $a-b \\in S\\}$. A graph is called integral, if all of its eigenvalues are integers. For an abelian group $\\Gamma$ we show that Cay$(\\Gamma,S)$ is integral, if $S$ belongs to the Boolean algebra $B(\\Gamma)$ generated by the subgroups of $\\Gamma$. The converse is proven for cyclic groups. A finite group $\\Gamma$ is called Cayley integral, if every undirected Cayley graph over $\\Gamma$ is integral. We determine all abelian Cayley integral groups.<\/jats:p>","DOI":"10.37236\/353","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:12:58Z","timestamp":1578715978000},"source":"Crossref","is-referenced-by-count":31,"title":["Integral Cayley Graphs over Abelian Groups"],"prefix":"10.37236","volume":"17","author":[{"given":"Walter","family":"Klotz","sequence":"first","affiliation":[]},{"given":"Torsten","family":"Sander","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2010,5,25]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r81\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r81\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:51:16Z","timestamp":1579305076000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1r81"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,5,25]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/353","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,5,25]]},"article-number":"R81"}}