certificate : keyword option of the form certificate=true or certificate=false.

Specifies whether a list representing the asteroidal triple should be returned in the event the graph contains an asteroidal triple. The default is false.

FindAsteroidalTriple(G) returns an asteroidal triple as a list of vertices of G if one exists, and NULL otherwise.

IsAsteroidalTripleFree(G) returns true if G does not contain an asteroidal triple, and false if it does.

An asteroidal triple for a graph G is a triple (u,v,w) of non-adjacent vertices of G such that for each pair from the triple, there exists a path between them that does not intersect the third vertex or any of its neighbors.

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

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

$C≔\mathrm{CycleGraph}\left(5\right)$

$C≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 5\; vertices\; and\; 5\; edge(s)}$

$\mathrm{FindAsteroidalTriple}\left(C\right)$

$P≔\mathrm{PetersenGraph}\left(\right)$

$P≔\mathrm{Graph\; 2:\; an\; undirected\; graph\; with\; 10\; vertices\; and\; 15\; edge(s)}$

$\mathrm{FindAsteroidalTriple}\left(P\right)$

$\left[2\,4\,6\right]$

The GraphTheory[FindAsteroidalTriple] and GraphTheory[IsAsteroidalTripleFree] commands were introduced in Maple 2024.

For more information on Maple 2024 changes, see Updates in Maple 2024.