Exact square coloring of graphs resulting from some graph operations and products

A vertex coloring of a graph G=(V,E) is called an exact square G if any pair vertices at distance 2 receive distinct colors. The minimum number colors required by the chromatic and denoted χ[#2](G). set clique are 2. G, ω[#2](G), maximum cardinality clearly, ω[#2](G)≤χ[#2](G). In this article, we give tight upper bounds various standard operations, including Cartesian product, strong lexicographic corona edge join, subdivision, Mycielskian graph. We also present lower these operations.