For two vertices $u$ and $v$ of a graph $G$, the closed interval $I[u,v]$ consists of $u$, $v$, and all vertices lying in some $u\text{--}v$ geodesic of $G$, while for $S\subseteq V\left(G\right)$, the set $I\left[S\right]$ is the union of all sets $I[u,v]$ for $u,v\in S$. A set $S$ of vertices of $G$ for which $I\left[S\right]=V\left(G\right)$ is a geodetic set for $G$, and the minimum cardinality of a geodetic set is the geodetic number $g\left(G\right)$. A vertex $v$ in $G$ is an extreme vertex if the subgraph induced by its neighborhood is complete. The number of extreme vertices in $G$ is its extreme order $\mathrm{e}x\left(G\right)$. A graph $G$ is an extreme geodesic...

A digraph in which any two vertices have distinct degree pairs is called irregular. Sets of degree pairs for all irregular oriented graphs (also loopless digraphs and pseudodigraphs) with minimum and maximum size are determined. Moreover, a method of constructing corresponding irregular realizations of those sets is given.