2-Power Domination in Certain Interconnection Networks

Abstract

Abstract The k-power domination problem generalizes domination and power domination problems. The k-power domination problem is to determine a minimum size vertex set S ⊆ V(G) such that after setting X = N[S] and iteratively adding to X vertices x that have a neighbour v in X such that at most k neighbours of v are not yet in X till we get X = V(G). The least cardinality of such set is called the k-power domination number of G and is denoted by γp,k (G). In this paper, we restrict our discussion to k = 2, referred to as 2-power domination. We compute 2-power domination number for certain interconnection networks such as hypertree, sibling tree, X-tree, Christmas tree, mesh, honeycomb mesh, hexagonal mesh, cylinder, generalized Petersen graph and subdivision of graphs.