Dergiler / Hacettepe Journal of Mathematics and Statistics / 2015 / Cilt: 44 Sayı: 5

Suborbital graphs for the group $\Gamma^2$

Suborbital graphs for the group $\Gamma^2$

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

Sayfa
1033–1044
DOI
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Abstract

In this paper, we investigate suborbital graphs formed by the action of Γ2 which is the group generated by the second powers of the elements of the modular group Γ on Qˆ. 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 Fu,N and show that it is connected if and only if N ≤ 2.