Induced H-packing k-partition of graphs
S. Maria Jesu Raja, Indra Rajasingh, Antony Xavier · International Journal of Computer Mathematics Computer Systems Theory · 2021
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 we prove that the induced K1,3-packing k-partition number of Qr is 2 for all hypercube networks with perfect K1,3-packing and prove that ipp(LQr)=4 for all locally twisted cubes with perfect K1,3-packing.