The independent neighbourhood number of a graph

Abstract

A set A of vertices in a graph G is a neighbourhood set, if G = U-v is an element of A < N [v] >, where <N [v] > is the subgraph of G induced by v and all vertices adjacent to v. A set A of vertices is independent if no two vertices in A are adjacent. The independent neighbourhood number n(i) (G) of G is the minimum number of vertices in an independent neighbourhood set of G. In this communication, bounds for n(i) (G), its exact values for some particular classes of graphs and some results concerning domination number have been found.