Abstract
Let [Formula: see text] be a connected simple graph. A dominating subset [Formula: see text] of [Formula: see text] is a fair dominating set of [Formula: see text] if all the vertices not in [Formula: see text] are dominated by the same number of vertices from [Formula: see text]. Let [Formula: see text] be a minimum fair dominating set of [Formula: see text]. A fair dominating set [Formula: see text] is called an inverse fair dominating set of [Formula: see text] with respect to [Formula: see text]. The inverse fair domination number of [Formula: see text] denoted by [Formula: see text] is the minimum cardinality of an inverse fair dominating set of [Formula: see text]. In this paper, we investigate the concept and give some important results. Further, we give the characterization of an inverse fair dominating set in the join and corona of two graphs.
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