IsSimplicial(G,v) returns true or false indicating whether the vertex v is simplicial.

A vertex v is simplicial if the subgraph induced by v and its neighbors forms a clique. That is, every pair of vertices which are both neighbors of v are also neighbors of each another.

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

$\mathrm{C4}≔\mathrm{CycleGraph}\left(4\right)$

$\mathrm{C4}≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 4\; vertices\; and\; 4\; edge(s)}$

$\mathrm{IsSimplicial}\left(\mathrm{C4}\,1\right)$

$\mathrm{false}$

$\mathrm{EG}≔\mathrm{Graph}\left(3\right)$

$\mathrm{EG}≔\mathrm{Graph\; 2:\; an\; undirected\; graph\; with\; 3\; vertices\; and\; 0\; edge(s)}$

$\mathrm{IsSimplicial}\left(\mathrm{EG}\,1\right)$

$\mathrm{true}$

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

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