Suborbital graphs for the group ?2

Abstract

In this paper, we investigate suborbital graphs formed by the action of?2which is the group generated by the second powers of the elementsof the modular group ? on ^Q. Firstly, conditions for being an edge,self-paired and paired graphs are provided, then we give necessary andsufficient conditions for the suborbital graphs to contain a circuit andto be a forest. Finally, we examine the connectivity of the subgraphFu,Nand show that it is connected if and only if N <= 2