IsReachable(G, u, v) returns a true when the vertex v is reachable from u in the graph G.

To produce an actual path (or directed path when G is directed) from u to v, use BellmanFordAlgorithm, DijkstrasAlgorithm, or ShortestPath.

To find all vertices reachable from u, use Reachable.

If G is an undirected graph, a vertex w is said to be reachable from a vertex v if there exists a path in G between v and w. This is true if and only if they are in the same connected component.

If G is a directed graph, a vertex w is said to be reachable from a vertex v if there exists a directed path in G from v to w.

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

$\mathrm{C6}≔\mathrm{CycleGraph}\left(6\right)$

$\mathrm{C6}≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 6\; vertices\; and\; 6\; edge(s)}$

$\mathrm{IsReachable}\left(\mathrm{C6}\,1\,5\right)$

$\mathrm{true}$

$\mathrm{ShortestPath}\left(\mathrm{C6}\,1\,5\right)$

$\left[1\,6\,5\right]$

$\mathrm{DP4}≔\mathrm{Graph}\left(\left[''A''\,''B''\,''C''\,''D''\right]\,\left\{\left[''A''\,''B''\right]\,\left[''B''\,''C''\right]\,\left[''C''\,''D''\right]\right\}\right)$

$\mathrm{DP4}≔\mathrm{Graph\; 2:\; a\; directed\; graph\; with\; 4\; vertices\; and\; 3\; arc(s)}$

$\mathrm{IsReachable}\left(\mathrm{DP4}\,''A''\,''D''\right)$

$\mathrm{true}$

$\mathrm{ShortestPath}\left(\mathrm{DP4}\,''A''\,''D''\right)$

$\left[''A''\,''B''\,''C''\,''D''\right]$

$\mathrm{IsReachable}\left(\mathrm{DP4}\,''D''\,''A''\right)$

$\mathrm{false}$

The GraphTheory[IsReachable] command was introduced in Maple 2018.

For more information on Maple 2018 changes, see Updates in Maple 2018.