We introduce the \emph{ Collatz conjecture} and its history. Some definition that this conjecture has, will be expressed and with these we try to explain some good lemma to justify the main properties of the \emph{ Collatz conjecture}. With these lemmas a situation made to go through to write some mainly properties of Collatz graph on $\mathbb{ Z}/10\mathbb{ Z}$. Then with something provided it will go to draw the graph on $\mathbb{ Z}/10\mathbb{ Z}$.
Categories: math.GM