IsOriented(G) returns true if G is a directed graph containing no symmtric pair of arcs. That is, for every pair of vertices u and v in G, at most one of the arcs [u,v] and [v,u] is in G.

Since a pair of symmetric arcs forms a directed cycle, every acyclic directed graph is oriented.

$\mathrm{with}\left(\mathrm{GraphTheory}\right)\:$

$\mathrm{G1}≔\mathrm{Digraph}\left(5\,\left\{\left[1\,2\right]\,\left[2\,3\right]\,\left[2\,4\right]\,\left[3\,5\right]\right\}\right)$

$\mathrm{G1}≔\mathrm{Graph\; 1:\; a\; directed\; graph\; with\; 5\; vertices\; and\; 4\; arc(s)}$

$\mathrm{IsOriented}\left(\mathrm{G1}\right)$

$\mathrm{true}$

$\mathrm{G2}≔\mathrm{Digraph}\left(5\,\left\{\left[1\,2\right]\,\left[2\,3\right]\,\left[2\,4\right]\,\left[3\,5\right]\,\left[4\,2\right]\right\}\right)$

$\mathrm{G2}≔\mathrm{Graph\; 2:\; a\; directed\; graph\; with\; 5\; vertices\; and\; 5\; arc(s)}$

$\mathrm{IsOriented}\left(\mathrm{G2}\right)$

$\mathrm{false}$

$\mathrm{G3}≔\mathrm{RandomGraphs}:-\mathrm{RandomArborescence}\left(100\right)$

$\mathrm{G3}≔\mathrm{Graph\; 3:\; a\; directed\; graph\; with\; 100\; vertices\; and\; 99\; arc(s)}$

$\mathrm{IsOriented}\left(\mathrm{G3}\right)$

$\mathrm{true}$

The GraphTheory[IsOriented] command was introduced in Maple 2022.

For more information on Maple 2022 changes, see Updates in Maple 2022.