Geodesic
Degree sequences of digraphs with highly irregular property
Discussiones Mathematicae. Graph Theory, Tome 18 (1998) no. 1, pp. 49-61

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A digraph such that for each its vertex, vertices of the out-neighbourhood have different in-degrees and vertices of the in-neighbourhood have different out-degrees, will be called an HI-digraph. In this paper, we give a characterization of sequences of pairs of out- and in-degrees of HI-digraphs.
Keywords: digraph, degree sequence, highly irregular property 
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Majcher, Zofia; Michael, Jerzy. Degree sequences of digraphs with highly irregular property. Discussiones Mathematicae. Graph Theory, Tome 18 (1998) no. 1, pp. 49-61. http://geodesic.mathdoc.fr/item/DMGT_1998_18_1_a3/