A comment on the bianchi groups

In this paper, we aim to discuss several the basic arithmetic structure of Bianchi groups. In particularly, we study fundamental domain and directed orbital graphs for the group PSL(2;O_1)

Some remarks on orbital digraphs for the finite primitive groups

In this paper we concern with the relationship between the finite groups PSL(2, q), q>5 a prime, and orbital digraphs. And also we explain that for a generator elliptic element in permutation group, there is a hyperbolic circuit in suborbital graph

Directed suborbital graphs on the Poincare disk

In this paper we investigate suborbital graphs of a special congruence subgroup of modular group. And this directed graphs is drawn in Poincare disk

On congruence equations arising from suborbital graphs

In this paper we deal with congruence equations arising from suborbital graphs of the normalizer of Γ_0(m) in PSL(2,R) . We also propose a conjecture concerning the suborbital graphs of the normalizer and the related congruence equations. In order to prove the existence of solution of an equation over prime finite field, this paper utilizes the Fuchsian group action on the upper half plane and Farey graphs properties

A remark on some fuchsian groups

In this paper we study combinatorial structures of some Fuchsian groups. We examine fundamental domains, group actions and genus for these groups

Congruence conditional signature problem

In this study, we examine properties of some subgroups of the modular group which can be characterized by algebraic and combinatoric. And also we investigate subgraphs of special congruence subgroup of modular group

General evaluation of suborbital graphs

In this paper, we aim to review suborbital graphs and also give an example to an extension of directed graphs

Circuit lengths of graphs for the Picard group

In this paper, we examine some properties of suborbital graphs for the Picard group. We obtain edge and circuit conditions, then propose a conjecture for the graph to be forest. This paper is an extension of some results in (Jones et al. in The Modular Group and Generalized Farey Graphs, pp. 316-338, 1991)

Digraphs on 3-dimensional hyperbolic space

In this paper we consider suborbital digraphs formed by the group action of the Bianchi groups. This study is an extension of digraphs on 3-dimensional hyperbolic upper half space. © 2018 Author(s)

Suborbital graphs of a extended congruence subgroup by Fricke involution

Let p be a fixed prime and let Gamma_0(p) denote the usual subgroup of PSL(2,Z) consisting of all the matrices with lower left entry divisible by p. Then the attached Fricke group is given by Gamma_0(p) ∪ Gamma_0(p) Wp. The Fricke group acts on the upper half-plane. Its action on Q∪{∞} is transitive but imprimitive. We study the action of Fricke group on the projective line Q∪{∞} by using suborbital graphs.These are directed graphs with vertex-set Q∪{∞}, their edge-sets being the orbits of the group on the cartesian square [Q∪{∞}]^2