Further results on equitable colorings of square of some special graphs

A graph [Formula: see text] is equitably [Formula: see text]-colorable if [Formula: see text] has a proper vertex coloring and the absolute difference in size between any distinct pairwise color classes is at most 1. The equitable chromatic number of [Formula: see text] denoted by [Formula: see text] is equitably [Formula: see text]-colorable} and the equitable chromatic threshold of [Formula: see text], denoted by [Formula: see text] min [Formula: see text] is equitably [Formula: see text]-colorable for all [Formula: see text]}. In this study, we derive exact values or bounds of the equitable chromatic number and the equitable chromatic threshold of the square of triangle snake graph, the square of alternate triangle snake graph, the square of triangular belt, the square of quadrilateral snake, the square of barbell graph, and the square of extended barbell graph.