The concept of dominating sets introduced by Ore and Berge, is
currently receiving much attention in the literature of graph
theory. Several types of domination parameters have been studied by
imposing several conditions on dominating sets. Ore observed that
the complement of every minimal dominating set of a graph with
minimum degree at least one is also a dominating set. This implies
that every graph with minimum degree at least one has two disjoint
dominating sets. Recently several authors initiated the study of
the cardinalities of pairs of disjoint dominating sets in graphs.
The inverse domination number is the minimum cardinality of a
dominating set whose complement contains a minimum dominating set.
Motivated by the inverse domination number, there are studies which
deals about two disjoint domination number of a graph.
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