Geodesic
On degree structure of graphs
Prikladnaya Diskretnaya Matematika. Supplement, no. 8 (2015), pp. 20-22.

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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.
Keywords: minimal primitive graph, graph degree structure. 
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     title = {On degree structure of graphs},
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V. M. Fomichev. On degree structure of graphs. Prikladnaya Diskretnaya Matematika. Supplement, no. 8 (2015), pp. 20-22. http://geodesic.mathdoc.fr/item/PDMA_2015_8_a6/

[1] Fomichev V. M., “Svoistva minimalnykh primitivnykh orgrafov”, Prikladnaya diskretnaya matematika, 2015, no. 2(28), 86–96