distance=integer or infinity

Specifies that the output should be limited to vertices reachable from v in the specified number of steps. Default is infinity.

output=one of graph, list, or set

Specifies whether the result should be a list or set of vertices reachable from v, or the subgraph induced by the vertices reachable from v. The default is list.

Reachable returns a list of all vertices reachable from the vertex v in the graph G.

To produce an actual spanning tree of vertices reachable from v, see SpanningTree or MinimalSpanningTree.

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.

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.

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

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

$\mathrm{C6}≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 6\; vertices\; and\; 6\; edges}$

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

$\left[1\,2\,3\,4\,5\,6\right]$

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

$G≔\mathrm{Graph\; 2:\; a\; directed\; graph\; with\; 5\; vertices\; and\; 6\; arcs}$

$\mathrm{Reachable}\left(G\,2\right)$

$\left[2\,3\right]$

$\mathrm{Reachable}\left(G\,2\,\mathrm{output}=\mathrm{graph}\right)$

$\mathrm{Graph\; 3:\; a\; directed\; graph\; with\; 2\; vertices\; and\; 1\; arc}$

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

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

The GraphTheory[Reachable] command was updated in Maple 2022.

The output option was introduced in Maple 2022.

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

The GraphTheory[Reachable] command was updated in Maple 2025.

The distance option was introduced in Maple 2025.

For more information on Maple 2025 changes, see Updates in Maple 2025.