distance=truefalse

Specifies whether to return the distance along with the common ancestor.

If true, the output of the command will be a two-element list, the first element of which is the ancestor vertex and the second of which is a list of distances from the input vertices to the common ancestor.

LowestCommonAncestors(G,u,v) returns a set of the lowest common ancestors of the vertices u and v in the directed graph G.

LowestCommonAncestors(G,C) returns a set of the lowest common ancestors of the vertices in C in the directed graph G.

LowestCommonDescendants(G,u,v) returns a set of the lowest common descendants of the vertices u and v in the directed graph G.

LowestCommonDescendants(G,C) returns a set of the lowest common descendants of the vertices in C in the directed graph G.

A vertex u is a common ancestor of a set C of vertices of G if it is an ancestor of each vertex in C.

A vertex u is a lowest common ancestor of a set C of vertices of G if it is a common ancestor of C and if none of its children are common ancestors of C

A common descendant and lowest common descendant are defined analogously to common ancestor and lowest common ancestor, substituting descendant for ancestor.

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

$G≔\mathrm{Graph}\left(8\,\left\{\left[1\,2\right]\,\left[1\,3\right]\,\left[3\,4\right]\,\left[3\,5\right]\,\left[5\,6\right]\,\left[5\,7\right]\,\left[7\,8\right]\right\}\right)$

$G≔\mathrm{Graph\; 1:\; a\; directed\; graph\; with\; 8\; vertices\; and\; 7\; arcs}$

$\mathrm{DrawGraph}\left(G\,\mathrm{style}=\mathrm{tree}\right)$

$\mathrm{LowestCommonAncestors}\left(G\,6\,8\right)$

$\left\{5\right\}$

$G≔\mathrm{GraphTheory}:-\mathrm{Graph}\left(5\,\left\{\left[1\,2\right]\,\left[1\,3\right]\,\left[2\,4\right]\,\left[2\,5\right]\,\left[3\,4\right]\,\left[3\,5\right]\right\}\,\mathrm{vertexpositions}=\left[\left[0\,1\right]\,\left[1\,2\right]\,\left[1\,0\right]\,\left[2\,2\right]\,\left[2\,0\right]\right]\right)$

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

$\mathrm{DrawGraph}\left(G\right)$

$\mathrm{LowestCommonAncestors}\left(G\,4\,5\right)$

$\left\{2\,3\right\}$

The GraphTheory[LowestCommonAncestors] and GraphTheory[LowestCommonDescendants] commands were introduced in Maple 2025.

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