On the Action of Γ0(N)\Gamma ^0(N) on Q^\hat{\mathbb{Q}}

In this paper we examine $\Gamma ^0(N)$-orbits on $\hat{\mathbb{Q}}$and the suborbital graphs for $\Gamma ^0(N)$. Each such suborbitalgraph is a disjoint union of subgraphs whose vertices form a blockof imprimitivity for $\Gamma ^0(N)$. Moreover, these subgraphs areshown to be vertex $\Gamma ^0(N)$-transitive and edge $\Gamma^0(N)$-transitive. Finally, necessary and sufficient conditions forbeing self-paired edge are provided

On the Action of Γ0(N)\Gamma ^0(N) on Q^\hat{\mathbb{Q}}

In this paper we examine $\Gamma ^0(N)$-orbits on $\hat{\mathbb{Q}}$and the suborbital graphs for $\Gamma ^0(N)$. Each such suborbitalgraph is a disjoint union of subgraphs whose vertices form a blockof imprimitivity for $\Gamma ^0(N)$. Moreover, these subgraphs areshown to be vertex $\Gamma ^0(N)$-transitive and edge $\Gamma^0(N)$-transitive. Finally, necessary and sufficient conditions forbeing self-paired edge are provided

On suborbital graphs and related continued fractions

In this paper, we study suborbital graphs for congruence subgroup Γ_0 (N) of the modular group Γ to have hyperbolic paths of minimal lengths. It turns out that these graphs give rise to a special continued fraction which is a special case of very famous fraction coming out from Pringsheim’s theorem

Suborbital graphs for the group ?2

In this paper, we investigate suborbital graphs formed by the action of?2which is the group generated by the second powers of the elementsof the modular group ? on ^Q. Firstly, conditions for being an edge,self-paired and paired graphs are provided, then we give necessary andsufficient conditions for the suborbital graphs to contain a circuit andto be a forest. Finally, we examine the connectivity of the subgraphFu,Nand show that it is connected if and only if N <=