Induced H -packing k -partition of graphs

The minimum induced H-packing k-partition number is denoted by ippH (G,H). The induced H-packing k-partition number denoted by ipp(G, H) is defined as ipp(G,H) = minippH (G,H) where the minimum is taken over all H-packings of G. In this paper, we obtain the induced P3 packing k-partition number for trees, slim trees, split graphs, complete
bipartite graphs, grids and circulant graphs. We also deal with networks having perfect K1,3-packing where K1,3 is a claw on four vertices. We prove that an induced K1,3-packing k-partition problem is NP-Complete. Further weprovethat the induced K1,3-packing k-partition number of Qr is 2 for all hypercubenetworkswithperfectK1,3-packing andprovethatipp(LQr) = 4 for all locally twisted cubes with perfect K1,3-packing