Neighborhood contraction in graphs

摘要

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 Nv 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.