Neighborhood contraction in graphs

Let G be a graph and v be any vertex of G. Then the neighborhood contracted graph G (v) of G, with respect to the vertex v, is the graph with vertex set V - N(v), where two vertices u,w a V - N(v) are adjacent in G (v) if either w = v and u is adjacent to any vertex of N(v) in G or u,w a parts per thousand N[v] and u,w are adjacent in G. The properties of the neighborhood contracted graphs are discussed in this paper. The neighborhood contraction in some special class of graphs, the domination in a graph and the neighborhood contracted graphs are discussed in the paper.