{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:12Z","timestamp":1753893792279,"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>A double-loop digraph $G(N;s_1,s_2)=G(V,E)$ is defined by  $V={\\bf Z}_N$ and $E=\\{(i,i+s_1), (i,i+s_2)|\\; i\\in V\\}$, for some   fixed steps $1\\leq s_1 &lt; s_2 &lt; N$ with $\\gcd(N,s_1,s_2)=1$.  Let $D(N;s_1,s_2)$ be the diameter of $G$ and let us define  $$ D(N)=\\min_{\\scriptstyle1\\leq s_1 &lt; s_2 &lt; N,\\atop\\scriptstyle\\gcd(N,s_1,s_2)=1}D(N;s_1,s_2),\\quad D_1(N)=\\min_{1 &lt; s &lt; N}D(N;1,s). $$ Some early works about the diameter of these digraphs studied the minimization of  $D(N;1,s)$, for a fixed value $N$, with $1 &lt;  s &lt; N$. Although the identity $D(N)=D_1(N)$ holds for infinite values of $N$,  there are also another infinite set of integers with  $D(N) &lt; D_1(N)$. These other integral values of $N$ are  called non-unit step integers or nus integers. In this work we give a characterization of nus integers and a  method for finding infinite families of nus integers is developed. Also the tight nus integers are classified. As a consequence of these results,  some errata and some flaws in the bibliography  are corrected.<\/jats:p>","DOI":"10.37236\/1695","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:30:05Z","timestamp":1578691805000},"source":"Crossref","is-referenced-by-count":5,"title":["Optimal Double-Loop Networks with Non-Unit Steps"],"prefix":"10.37236","volume":"10","author":[{"given":"F.","family":"Aguil\u00f3","sequence":"first","affiliation":[]},{"given":"E.","family":"Sim\u00f3","sequence":"additional","affiliation":[]},{"given":"M.","family":"Zaragoz\u00e1","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2003,1,6]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v10i1r2\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v10i1r2\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T00:10:24Z","timestamp":1579306224000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v10i1r2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,1,6]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2003,1,6]]}},"URL":"https:\/\/doi.org\/10.37236\/1695","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2003,1,6]]},"article-number":"R2"}}