On quadrilaterals in the suborbital graphs of the normalizer

Abstract

n this paper‎, ‎we investigate suborbital graphs formed by $Nbig(Gamma_0(N)big)$-invariant equivalence relation induced on $hat{mathbb{Q}}$‎. ‎Conditions for being an edge are obtained as a main tool‎, ‎then necessary and sufficient conditions for the suborbital graphs to contain a circuit are investigated‎.