Abstract

Let (G, R) denote the directed graph obtained from undirected graph G by an acyclic orientation R so that (G, R) contains no directed cycle. We consider acyclic orientations R of a unicyclic graph G which maximizes/minimizes the number of ordered pairs of non-adjacent vertices with directed paths in (G, R). These orientations are referred as optimal orientations. We present algorithms to determine optimal orientations of a unicyclic graph.

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