Total Dominator Coloring of the Hypercube Q_{2^n}

A proper coloring of the vertices of a graph G is called a total dominator coloring if every vertex of G is adjacent to all vertices of at least one color class.The total dominator chromatic number of G, denoted by χ t d (G), is the minimum number of color classes required in such a coloring.In this paper, the total dominator chromatic number of the hypercube Q2n is determined for n ≥ 3. Also, algorithms are developed to obtain the maximum number 2 n of disjoint total dominating sets in Q2n for n = 3 and n = 4.A notable feature of this study is the introduction and utilization of novel combinatorial structures termed semi-Latin squares, pairs of mate semi-Latin squares, and chess Latin squares, which play a crucial role in constructing the corresponding colorings and domination partitions.