Graph Labelling

You are given a directed graph $G$ with $N$ vertices (numbered $1$ through $N$) and $M$ edges. Let's denote the set of its vertices by $V$, the set of its edges by $E$ and an edge from a vertex $u$ to a vertex $v$ by $(u, v)$. Then, let's define: - For each $u, v \in V$, $R(u, v)$ is true if $v$ can be reached from $u$ or false otherwise. Specifically, if $u = v$, it is always true. - For each $