Independent domination and vertex coloring in graphs

Let [Formula: see text] be a graph of order [Formula: see text]. Let [Formula: see text] and [Formula: see text] denote respectively the independent domination number, independence number and chromatic number of [Formula: see text] These parameters satisfy the well known inequality [Formula: see text]. In this paper we determine conditions under which the above inequalities become equalities and use these conditions to determine extremal graphs in some specific graph classes.