Induced H-packing k-partition of graphs. Issue 2 (3rd April 2021) - Raja, S. Maria Jesu; Rajasingh, Indra; Xavier, Antony
ABSTRACT: The minimum induced H -packing k -partition number is denoted by i p p H ( G, H ) . The induced H -packing k -partition number denoted by i p p ( G, H ) is defined as i p p ( G, H ) = m i n i p p H ( G, H ) where the minimum is taken over all H -packings of G . In this paper, we obtain the induced P 3 -packing k -partition number for trees, slim trees, split graphs, complete bipartite graphs, grids and circulant graphs. We also deal with networks having perfect K 1, 3 -packing where K 1, 3 is a claw on four vertices. We prove that an induced K 1, 3 -packing k -partition problem is NP -Complete. Further we prove that the induced K 1, 3 -packing k -partition number of Q r is 2 for all hypercube networks with perfect K 1, 3 -packing and prove that i p p ( L Q r ) = 4 for all locally twisted cubes with perfect K 1, 3 -packing.