THE k-INDEPENDENT GRAPH OF A GRAPH

Let G = (V, E) be a simple graph.A set I ⊆ V is an independent set, if no two of its members are adjacent in G.The k-independent graph of G, I k (G), is defined to be the graph whose vertices correspond to the independent sets of G that have cardinality at most k.Two vertices in I k (G) are adjacent if and only if the corresponding independent sets of G differ by either adding or deleting a single vertex.In this paper, we obtain some properties of I k (G) and compute it for some graphs.