Suborbital graphs for the group ?2

In this paper, we investigate suborbital graphs formed by the action of ?2 which is the group generated by the second powers of the elements of the modular group ? on Q. 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. © 2015, Hacettepe Journal of Mathematics and Statistics. All rights reserved