Graphs and codes produced by a new method for dividing a natural number by two

Abstract

In this paper, we introduce a new method which we call it MZ-method, for dividing a natural number $x$ by two and then we use graph as a model to show MZ-algorithm. Applying (recursively) $k$-times of the MZ-method for the number $x$, produces a graph with unique structure that is denoted by $G_k(x)$. We investigate the structure of $G_k(x)$. Also from the natural number $x$ and graph $G_k(x)$ we produce codes which are important and applicable in the information security and cryptography.