Induced H-Packing k-Partition Problem in Certain Networks

A collection = {H1 ,H2 ,..., Hr } of induced sub graphs of a graph G is said to be sg-independent if (i) V(Hi ) V(Hj )= , i j, 1≤ i, j≤ r and (ii) no edge of G has its one end in Hi and the other end in Hj , i j, 1≤ i, j≤ r. If Hi H, ∀ i, 1≤ i ≤r, then is referred to as a H-independent set of G. Let be a perfect or almost perfect H-packing of a graph G. Finding a partition of such that is Hindependent set, ∀ i, 1 ≤ i ≤ k, with minimum k is called the induced H-packing kpartition problem of G. The induced H-packing k-partition number denoted by ipp(G,H) is defined as ipp(G,H) = min (G,H) where the minimum is taken over all H-packing of G. In this paper we obtain the induced H-packing k-partition number for Enhanced hypercube, Augmented Cubes and Crossed Cube networks where H is isomorphic to and .