Minimal primitive extensions of oriented graphs

(Oriented) graph $G=(V,\alpha)$ is called primitive if there exists an integer $r\ge 1$ such that every two vertices can be connected by a route of length $r$. A graph $G'=(V,\alpha)$ is said to be a primitive extension of $G$ if $G'$ is primitive and $\alpha\subseteq\alpha'$. Primitive extensions with a minimal possible number of additional arcs are constructed for some acyclic graphs (trees, linear and polygonal graphs).