Abstract
In this paper, we investigate suborbital graphs generated by the action of the group \(\varGamma ^{3}\) which is the group obtained from the third powers of the elements of the modular group \(\varGamma \) on \(\mathbb {Q}\cup \{\infty \}\). First, we give necessary and sufficient conditions for an edge to be in the related graphs. Then, we investigate connectedness of the graphs.
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