- Hacettepe Journal of Mathematics and Statistics
- Vol: 44 Issue: 5
- Suborbital graphs for the group $\Gamma^2$
Suborbital graphs for the group $\Gamma^2$
Authors : Bahadır Özgür Güler, Murat Beşenk, Yavuz Kesicioğlu, Ali Hikmet Değer
Pages : 1033-1044
View : 17 | Download : 8
Publication Date : 2015-10-01
Article Type : Research
Abstract :In this paper, we investigate suborbital graphs formed by the action of Γ 2 which is the group generated by the second powers of the elements of the modular group Γ on Q ˆ . Firstly, conditions for being an edge, self-paired and paired graphs are provided, then we give necessary and sufficient conditions for the suborbital graphs to contain a circuit and to be a forest. Finally, we examine the connectivity of the subgraph F u,N and show that it is connected if and only if N ≤ 2 .Keywords : Modular group, Group action, Suborbital graphs