A chess board of size m x n can be translated to a Queen's graph in which vertices are adjacent if their squares on the board are in the same row, column, or diagonal. In this research, the total dominator coloring of a Queen's graph is explored, yielding a conjecture for the general m x n case.
Smith, Fiona, "Total Dominator Coloring on the Queen's graph" (2023). Celebrating Scholarship and Creativity Day (2018-). 212.