Suborbital graphs for the group $\Gamma^2$

Authors : Bahadır Özgür GÜLER, Murat BEŞENK, Yavuz KESİCİOĞLU, Ali Hikmet DEĞER

Pages : 1033-1044

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Publication Date : 2015-10-01

Article Type : Research Paper

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