A NEW CONSTRUCTION FOR VERTEX DECOMPOSABLE GRAPHS

Let G be a finite simple graph on the vertex set V (G) and let S subset of V (G). Adding a whisker to G at x means adding a new vertex y and edge xy to G where x is an element of V (G). The graph G boolean OR W(S) is obtained from G by adding a whisker to every vertex of S. We prove that if G \ S is either a graph with no chordless cycle of length other than 3 or 5, chordal graph or C-5, then G boolean OR W(S) is a vertex decomposable graph.