\begin{definition}[Definition:Cut-Vertex]
Let $G = \struct {V, E}$ be a connected graph.
Let $v$ be a vertex of $G$.
Then $v$ is a '''cut-vertex''' of $G$ {{iff}} the vertex deletion $G - v$ is a vertex cut of $G$.
That is, such that $G - v$ is disconnected.
Thus, a '''cut-vertex''' of $G$ is a singleton vertex cut of $G$.
\end{definition}