{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:39Z","timestamp":1753893819247,"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>In this study, we deal with the conjecture given in [R. Keskin, Suborbital graph for the normalizer of $\\Gamma _{0}(m)$, European Journal of Combinatorics 27 (2006) 193-206.], that when the normalizer of $\\Gamma _{0}(N)$ acts transitively on ${\\Bbb Q\\cup\\{\\infty \\}}$, any circuit in the suborbital graph $G(\\infty,u\/n)$ for the normalizer of $\\Gamma _{0}(N),$ is of the form  $$ v\\rightarrow T(v)\\rightarrow T^{2}(v)\\rightarrow {\\ \\cdot \\cdot \\cdot } \\rightarrow T^{k-1}(v)\\rightarrow v, $$  where $n&gt;1$, $v\\in {\\Bbb Q\\cup \\{\\infty \\}}$ and $T$ is an elliptic mapping of order $k$ in the normalizer of $\\Gamma_{0}(N)$.<\/jats:p>","DOI":"10.37236\/205","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:25:07Z","timestamp":1578716707000},"source":"Crossref","is-referenced-by-count":6,"title":["On Suborbital Graphs for the Normalizer of $\\Gamma_{0}(N)$"],"prefix":"10.37236","volume":"16","author":[{"given":"Refik","family":"Keskin","sequence":"first","affiliation":[]},{"given":"Bahar","family":"Demirt\u00fcrk","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2009,9,18]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r116\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r116\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T02:40:47Z","timestamp":1579315247000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1r116"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,9,18]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/205","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2009,9,18]]},"article-number":"R116"}}