Triangles in the suborbital graphs of the normalizer of $\Gamma_0(N)$

Abstract

<p>In this paper, we investigate a suborbital graph for the normalizer of Γ<sub>0(<em>N</em>)</sub> ∈ PSL(2;<em>R</em>), where <em>N</em> will be of the form 2<sup>4</sup><em>p</em><sup>2</sup> such that <em>p</em> > 3 is a prime number. Then we give edge and circuit conditions on graphs arising from the non-transitive action of the normalizer.</p>