# isSheddingVertex -- determines whether a vertex of a simplicial complex is a shedding vertex

## Synopsis

• Usage:
isSheddingVertex(x, S)
• Inputs:
• x, , a vertex of $S$
• S, ,
• Outputs:
• B, , true if and only if $x$ is a shedding vertex of $S$

## Description

Definition 11.1 of [BW-2] states that a shedding vertex $x$ of a simplicial complex $S$ is a vertex such that the link and face deletion of $x$ from $S$ are vertex decomposable and share no common facets.

 i1 : R = QQ[a..f]; i2 : S = simplicialComplex {a*b*c, c*d, d*e, e*f, d*f}; i3 : isSheddingVertex(a, S) o3 = false i4 : isSheddingVertex(f, S) o4 = true