Volume 11 β’ Issue 2 β’ PP: 50-59 β’ 2024
The Dominator Coloring of Some Graph Classes
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A proper vertex coloring of a graph πΊ(π,πΈ) is an assignment of colors to the vertices of πΊ so that no two adjacent vertices have the same color. A dominator coloring of πΊ 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 πΊ is called the dominator coloring number and is denoted by ππ(πΊ). In this paper, we determine the dominator coloring number of strong grid graphs ππβ ππ when π,π≥3. We also determine the dominator coloring number of the Queen graph π2,π for π≥2.
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References
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