An introduction to proper-coupled-domination in graphs
Suk J. Seo, Peter J. Slater · 2006
In this paper we introduce the proper-coupled-domination problem. Specifically, assume that we have (disjoint) subsets S1, S2, ..., St of the vertex set V(G) of graph G. One seeks to find the minimum cardinality of a dominating set D with the property that D ∩ Si ≠ φ implies that Si ⊆ D for 1 ≤ i ≤ t. We focus, in particular, on a coupled-domination parameter for which each Si has cardinality at most two.