Neighborhood contraction in graphs

Abstract

Let G be a graph and v be any vertex of G. Then the neighborhood contracted graphG<inf>v</inf> of G, with respect to the vertex v, is the graph with vertex set V ? N(v), where two vertices u,w ? V ? N(v) are adjacent in G<inf>v</inf> if either w = v and u is adjacent to any vertex of N(v) in G or u,w ? 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. © 2015, The Indian National Science Academy.