INVERSE BLOCK DOMINATION AND RELATED PARAMETERS IN GRAPHS

The concept of inverse domination was introduced by V.R. Kulli and S.C. Sigarakanti. Given a graph G, let D represent a γ-set of G. A dominating set D₁ ⊆ V − D is termed an inverse dominating set of G with respect to D. The inverse domination number, denoted by γ^′ (G), is the cardinality of the smallest inverse dominating set. Although inverse domination has been widely explored, the literature provides relatively few bounds on this parameter. Several bounds have been established in terms of graph parameters such as order, size, maximum degree, and domatic number. Additionally, various inverse block domination parameters have been introduced, with initial studies examining their properties. In this paper, we derive an upper bound for the inverse domination number of a graph in terms of its domatic number. Furthermore, a lower bound is provided in terms of the graph’s order and size.