aspg-33-3343-1792222686 20261017073806 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 2024 11 2 Ramazan Yasar Ankara University, Engineering Faculty, Department of Artificial Intelligence and Data Engineering, Ankara, Turkey 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 50 59 3343 https://creativecommons.org/licenses/by/4.0/ 10.54216/GJMSA.0110207 https://americaspg.com/journal/33/article/3343 https://americaspg.com/storage/91733053037.pdf