On equitable near-proper coloring of some derived graph classes

An equitable near-proper coloring of a graph $G$ is a defective coloring in which the number of vertices in any two color classes differ by at most one and the bad edges obtained is minimised by restricting the number of color classes that can have adjacency among their own elements. This paper investigates the equitable near-proper coloring of some derived graph classes like Mycielski graphs, splitting graphs and shadow graphs.