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On oriented graph scores. (English) Zbl 1199.05154

The score of a vertex \(v\) in an oriented graph on \(n\) vertices is \(a_v=n - 1 + d_v^+ -d_v^-\), where \(d_v^+\) and \(d_v^-\) are outdegree and indegree of \(v\), respectively. The set of distinct scores of the vertices in an oriented graph is called a score set.
The authors give new proof of a known result of P. Avery giving necessary and sufficient conditions for a non-negative sequence of integers to be a score in an oriented graph.

MSC:

05C20 Directed graphs (digraphs), tournaments