Parameterized Complexity of Paired Domination

The Paired Domination problem is one of the well-studied variants of the classical Dominating Set problem. In a graph G on n vertices, a dominating set D (set of vertices such that \(N[D]=V(G)\) ) is called a paired dominating set of G, if G[D] has perfect matching. In the Paired Domination problem, given a graph G and a positive integer k, the task is to check whether G has a paired dominating set of size at most k. The problem is a variant of the Dominating Set problem, and hence inherits most of the hardness of the Dominating Set problem; however, the same cannot be said about the algorithmic results. In this paper, we study the problem from the perspective of parameterized complexity, both from solution and structural parameterization, and obtain the following results.