Induced H-Packing k-Partition Problem in Certain Networks

Induced H-Packing k-Partition Problem in Certain Networks Department of Mathematics, Loyola College, University of Madras, Chennai - 034,India. Santiagu Theresal* Antony Xavier Department of Mathematics, Loyola College, University of Madras, Chennai - 034, India S. Maria Jesu Raja Department of Mathematics, Vels Institute of Science, Technology and Advanced Studies, Chennai -117, India.

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 H-independent set, ∀ i, 1 ≤ i ≤ k, with minimum k is called the induced H-packing k-partition 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 .
09 30 2019 1003 1010 CC-BY-NC-ND 4.0 10.35940/BEIESP.CrossMarkPolicy www.ijrte.org true 10.35940/ijrte.C4062.098319 https://www.ijrte.org/portfolio-item/C4062098319/ https://www.ijrte.org/wp-content/uploads/papers/v8i3/C4062098319.pdf