Suborbital Graphs For a Non-Transitive Action of The Normalizer

Abstract

In this paper, we investigate suborbital graph for the normalizer of $\Gamma _0(N)$ in$PSL(2,\mathbb{R})$, where $N$ will be of the form $3^2p^2$, $p$ is a prime and $p>3$. Then we give edge and circuit conditions on graphs arising from the non-transitive action of the normalizer.