resulting oriented graph the *converse* of $\overrightarrow{D}$ and denote it $\overrightarrow{D}^*$. For a graph $D$ with vertex $v$, the [*deletion of v*]{} is an operation that yields a graph with vertex set $ V(D) \setminus v$ and edge set $E(D) \setminus \{e_1, e_2,...,e_k \}$, such that $e_i$, $1 \le i \le k$, is incident to $v$. We denote the graph $D$ with vertex $v$ deleted as $D-v$. The deletion of a vertex $v$ in an oriented graph $\overrightarrow{D}$ is defined analogously and is denoted $\overrightarrow{D}-v$.

For $n \in \mathbb{N}$, let $[n]$ denote $ \{ 1,2,...,n \}$. For $n \geq 2$, the standard path, denoted $P_n$, is the graph with $V(P_n) = \{i \, \vert \, i \in [n] \}$ and $E(P_n)$ consisting of the edges with endpoints $i$, $i+1$ for $1 \le i \le n-1$. A [*path on $n$ vertices*]{} (resp. an [*n-path*]{}) is a graph isomorphic to $P_n$ (for some $n$). A graph is *connected* if each pair of vertices belongs to a path; an oriented graph is connected if its underlying graph is connected. If a graph is not connected, it is *disconnected* and its maximal connected subgraphs are called *components*. The standard cycle, denoted $C_n$, is the 