Abstract
The degree setD D of a digraphD is the set of outdegrees of the vertices ofD. For a finite, nonempty setS of nonnegative integers, it is shown that there exists an asymmetric digraph (oriented graph)D such thatD D =S. Furthermore, the minimum order of such a digraphD is determined. Also, given two finite sequences of nonnegative integers, a necessary and sufficient condition is provided for which these sequences are the outdegree sequences of the two sets of an asymmetric bipartite digraph.
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S. F. Kapoor, A. D. Polimeni andC. E. Wall, Degree sets for graphs (to appear).
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Chartrand, G., Lesniak, L. & Roberts, J. Degree sets for digraphs. Period Math Hung 7, 77–85 (1976). https://doi.org/10.1007/BF02019997
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DOI: https://doi.org/10.1007/BF02019997