On degree structure of graphs

The paper presents some properties of degree structure for different classes of digraphs and describes degree structure for primitive digraphs with $n$ vertices and $n+1$ and $n+2$ arcs. For any integer $n\ge5$ and $k\in\{2,\dots,n-3\}$, the existence of a minimal primitive digraph with $n$ vertices, $n+k$ arcs and degree structure $\{(1,1)^{n-1},(k+1,k+1)^1\}$ is shown.