Circuits in Suborbital Graphs for The Normalizer

Abstract

In this paper, we investigate suborbital graph for the normalizer of $$\varGamma _0(N)$$ in $$PSL(2,\mathbb {R})$$ , where N will be of the form $$2^23p^2$$ , p is prime number greater than 3 and $$p\equiv 1\pmod {3}$$ . Then we give edge and circuit conditions on graphs arising from the imprimitive action of the normalizer.