Geodesic
A Note on Degree Sequences of Graphs
Canadian mathematical bulletin, Tome 23 (1980) no. 1, pp. 21-27

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Sufficient conditions for a sequence of numbers to be the degree sequence of a graph are derived from the Erdos-Gallai theorem on degree sequences of graphs. 
Brualdi, Richard A. A Note on Degree Sequences of Graphs. Canadian mathematical bulletin, Tome 23 (1980) no. 1, pp. 21-27. doi: 10.4153/CMB-1980-003-5
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