Neighbourhood graph of a graph and its Excellence

Claude Berge in 1980 introduced B-graphs. There are graphs in which every vertex in the graph is contained in a maximum independent set of the graph. Fricke et al in 2002 made a beginning of the study of graphs which are excellent with respect to various graph parameters. A graph is neighbourhood excellent if every vertex in the graph is contained in a neighbourhood set. Given a graph, a new graph can be constructed by using neighbourhood sets of G. The vertices of the new graph are of course the neighbourgood sets of G and two such vertices will be adjacent if in the corresponding neighborhood sets, one can move from one of them to other by deletion of a vertex and addition of another vertex. This book is devoted to the study of Neighbourhood graph of a graph and its Excellence.