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 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.