IsSimplicial - Maple Help

GraphTheory

 IsSimplicial
 determine if a vertex is simplicial

 Calling Sequence IsSimplicial(G, v)

Parameters

 G - graph v - vertex of the graph

Description

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

Definition

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{GraphTheory}\right):$
 > $\mathrm{C4}≔\mathrm{CycleGraph}\left(4\right)$
 ${\mathrm{C4}}{≔}{\mathrm{Graph 1: an undirected graph with 4 vertices and 4 edge\left(s\right)}}$ (1)
 > $\mathrm{IsSimplicial}\left(\mathrm{C4},1\right)$
 ${\mathrm{false}}$ (2)
 > $\mathrm{EG}≔\mathrm{Graph}\left(3\right)$
 ${\mathrm{EG}}{≔}{\mathrm{Graph 2: an undirected graph with 3 vertices and 0 edge\left(s\right)}}$ (3)
 > $\mathrm{IsSimplicial}\left(\mathrm{EG},1\right)$
 ${\mathrm{true}}$ (4)

Compatibility

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