This paper proves a conjecture of G. A. Jones, D. Singerman and K. Wicks, that a suborbital graph for the modular group is a forest if and only if it contains no triangles.

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In this paper we show that the subgraph F 3 is disconnected and that for all integers m, we find all integers a and b such that (9m 2 -4)a 2 + 4 and 5b 2 ± 4 are square. It turns out that the set of numbers b comprises the Fibonacci numbers.

In this paper, we give necessary and sufficient conditions for the graph H u,n to be connected and a forest.