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A subset D of the vertex set of a graph G, is a dominating set if every vertex in − is adjacent to at least one vertex in D. The domination number () is the minimum cardinality of a dominating set of G. A subset of −, which is also a dominating set of G is called an inverse dominating set of G with respect to D. The inverse domination number () is the minimum cardinality of the inverse dominating sets. Domke et al. (2004) characterized connected graphs G with ()

Graphs with Constant Sum of Domination and Inverse Domination Numbers