Plik:GraphGoddnumbers.png

Definition of the graph G

[math] \color{blue}G=\langle V,E \rangle [/math]

The set of all odd natural numbers constitutes the set [math]V[/math].

A pair [math]\langle n,m\rangle [/math] of odd numbers is an edge iff [math]n[/math] is indivisible by 3 and there exists the natural number [math]i\gt0[/math] such that [math]\color{blue} m=\frac{n\cdot 2^{2i-(n \mod 3)-1}-1}{3}[/math]

Lemma

The graph [math]G[/math] is a tree iff the graph [math]HC[/math] is a tree.