a new construction for vertex decomposable graphs

Let g be a finite simple graph on the vertex set v(g) and let s subseteq v(g) . adding a whisker to g at x means adding a new vertex y and edge xy to g where x in v(g) . the graph gcup w(s) is obtained from g by adding a whisker to every vertex of s. we prove that if g setminus s is either a graph with no chordless cycle of length other than 3 or 5, chordal graph or c_5, then g cup w(s) is a vertex decomposable graph.