Induced H-Packing k-Partition Problem in Certain Networks
Santiagu Theresal1, Antony Xavier2, S. Maria Jesu Raja3
1Santiagu Theresal*, Department of Mathematics, Loyola College, University of Madras, Chennai – 034,India.
2Antony Xavier, Department of Mathematics, Loyola College, University of Madras, Chennai – 034, India.
3S. Maria Jesu Raja, Department of Mathematics, Vels Institute of Science, Technology and Advanced Studies, Chennai -117, India.
Manuscript received on 15 August 2019. | Revised Manuscript received on 25 August 2019. | Manuscript published on 30 September 2019. | PP: 1003-1010 | Volume-8 Issue-3 September 2019 | Retrieval Number: C4062098319/19©BEIESP | DOI: 10.35940/ijrte.C4062.098319
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Abstract: A collection 𝑡 = {H1,H2,…, Hr } of induced sub graphs of a graph G is said to be sg-independent if (i) V(Hi)∩V(Hj )= Φ, i G j, 1≤ i, j≤ r and (ii) no edge of G has its one end in Hi and the other end in Hj , i Gj, 1≤ i, j≤ r. If Hi H, ∀ i, 1≤ i ≤r, then 𝑡 is referred to as a H-independent set of G. Let 𝐻 be a perfect or almost perfect H-packing of a graph G. Finding a partition {𝐻1, 𝐻2, . . . 𝐻𝑘 } of V such that Vi 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 i𝑝𝑝V (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 𝑃3 and 𝐶4.
Keywords: Augmented Cubes, Crossed Cube Networks, Enhanced hypercube, Induced H-packing k-partition..
Scope of the Article: Augmented Reality