On Induced Matching Partitions of Certain Interconnection Networks

The induced matching partition number of a graph G, denoted by imp(G), is the minimum integer k such that V(G) has a k-partition (V1, V2 ... Vk ) such that, for each i, 1 ≤ i ≤ k, G[Vi], the subgraph of G induced by Vi, is a 1-regular graph. The induced matching k-partition problem is NP-complete even for k = 2. In this paper we investigate the induced matching partition problem for butterfly networks. We identify hypercubes, cube-connected cycles, grids of order m x n, where at least one of m and n is even, as graphs for which imp(G) = 2. In the sequel we prove that imp(G) does not exist for grids of order m x n where m and n are both odd and Mesh of trees MT(n), n ≥ 2.