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The (directed) distance from a vertex $u$ to a vertex $v$ in a strong digraph $D$ is the length of a shortest $u$-$v$ (directed) path in $D$. The eccentricity of a vertex $v$ of $D$ is the distance from $v$ to a vertex furthest from $v$ in $D$. The radius rad$D$ is the minimum eccentricity among the vertices of $D$ and the diameter diam$D$ is the maximum eccentricity. A central vertex is a vertex with eccentricity $\mathrm{r}adD$ and the subdigraph induced by the central vertices is the center $C\left(D\right)$. For a central vertex $v$ in a strong digraph...

For a vertex $v$ in a graph $G$, the set $N_2\left(v\right)$ consists of those vertices of $G$ whose distance from $v$ is 2. If a graph $G$ contains a set $S$ of vertices such that the sets $N_2\left(v\right)$, $v\in S$, form a partition of $V\left(G\right)$, then $G$ is called a $2$-step domination graph. We describe $2$-step domination graphs possessing some prescribed property. In addition, all $2$-step domination paths and cycles are determined.