On the Shannon capacity of a directed graph
The Shannon capacity of an undirected graph G, t(G), is \(t(G)=\sup^ k\sqrt{\alpha (G^ k)}\), \(k\in N\), where \(\alpha\) (G) is the vertex independence number of G and \(G^ k\) the Cartesian product of G by itself k times. The authors extend naturally the definition for directed graphs and show that if G is a directed cycle of length n then \(t(G)=n-1\) and \(t(G)=| V(G)|\) for every cycle-free digraph G.
scientific article; zbMATH DE number 3948304