{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T12:10:27Z","timestamp":1778242227896,"version":"3.51.4"},"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>An almost Moore digraph is a diregular digraph of degree $d&gt;1$, diameter $k&gt;1$ and order $d+d^2+ \\cdots +d^k$. Their existence has only been shown for $k=2$. It has also been conjectured that there are no more almost Moore digraphs, but so far their nonexistence has only been proven for $k=3,4$ and for $d=2,3$ when $k\\geq 3$.\r\nIn this paper we study the structure of the subdigraphs of an almost Moore digraph induced by the vertices fixed by an automorphism determined by a power of the permutation $r$ of repeats of the digraph. We deduce that each almost Moore digraph of degree $d$ and diameter $k$ with self-repeats has such a subdigraph whose vertices have order $\\leq d-1$ under $r$. From this, we extend the results about the nonexistence of almost Moore digraphs with self-repeats of degrees 4 and 5 to those whose diameter is large enough with respect to the degree. More precisely, we prove their nonexistence when $k\\geq 2(d-1)$ if $k$ is odd and when $k \\geq 2(d-1)^2$ if $k$ is even. We also show that these findings jointly with other results imply that there are no almost Moore digraphs with self-repeats for degrees $d$, $6\\leq d\\leq 12$, and $k&gt;2$.<\/jats:p>","DOI":"10.37236\/13564","type":"journal-article","created":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T11:31:04Z","timestamp":1778239864000},"source":"Crossref","is-referenced-by-count":0,"title":["On the Nonexistence of Almost Moore Digraphs with Self-Repeats"],"prefix":"10.37236","volume":"33","author":[{"given":"Arnau","family":"Messegu\u00e9","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Josep M.","family":"Miret","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anita A.","family":"Sillasen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2026,5,8]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i2p27\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i2p27\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T11:31:04Z","timestamp":1778239864000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v33i2p27"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,8]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2026,4,14]]}},"URL":"https:\/\/doi.org\/10.37236\/13564","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,8]]},"article-number":"P2.27"}}