@article{article_524323, title={Suborbital graphs for the group $\Gamma^2$}, journal={Hacettepe Journal of Mathematics and Statistics}, volume={44}, pages={1033–1044}, year={2015}, author={Güler, Bahadır Özgür and Beşenk, Murat and Kesicioğlu, Yavuz and Değer, Ali Hikmet}, keywords={Modular group,Group action,Suborbital graphs}, abstract={<div class="page" title="Page 1" style="font-family: -webkit-standard;"> <div class="layoutArea"> <div class="column"> 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 . </div> </div> </div>}, number={5}, publisher={Hacettepe University}