On equitable near proper coloring of certain graph classes

The non-availability of sufficient number of colors to color a graph leads to defective coloring problems. Coloring a graph with insufficient number of colors cause the end vertices of some edges receive the same color. Such edges with same colored end vertices are called as bad edges. The minimum number of bad edges obtained from an equitable near proper coloring of a graph G is known as equitable defective number. In this paper, we discuss the equitable near proper coloring of some families of graphs and we also determine the equitable defective number for the same.