Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 10.54216/GJSMA https://www.americaspg.com/journals/show/3343 2022 2022 Ankara University, Engineering Faculty, Department of Artificial Intelligence and Data Engineering, Ankara, Turkey Ramazan Ramazan A proper vertex coloring of a graph 𝐺(𝑉,𝐸) is an assignment of colors to the vertices of 𝐺 so that no two adjacent vertices have the same color. A dominator coloring of 𝐺 is a proper vertex coloring for which every vertex is adjacent to all the vertices of at least one color class. The minimum number of colors required to establish a proper dominator coloring on 𝐺 is called the dominator coloring number and is denoted by 𝜒𝑑(𝐺). In this paper, we determine the dominator coloring number of strong grid graphs 𝑃𝑚⊠𝑃𝑛 when 𝑚,𝑛≥3. We also determine the dominator coloring number of the Queen graph 𝑄2,𝑛 for 𝑛≥2. 2024 2024 50 59 10.54216/GJMSA.0110207 https://www.americaspg.com/articleinfo/33/show/3343