An introduction to proper-coupled-domination in graphs

Abstract

In this paper we introduce the proper-coupled-domination problem. Specifically, assume that we have (disjoint) subsets S 1 , S 2 , . . . , S t 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 ∩ S i ≠ φ implies that S i ⊆ D for 1 ≤ i ≤ t. We focus, in particular, on a coupled-domination parameter for which each S i has cardinality at most two.