In this thesis, we study the problem of total dominator coloring of graphs,
which combines elements of graph coloring and domination. We focus on
several important classes of graphs, such as trees, cographs, chain graphs,
split graphs, bipartite graphs, and planar graphs. We investigate how the
problem arises within these classes, analyze its computational complexity,
and identify cases where it can be solved efficiently. The aim of the thesis is
to present fundamental results, highlight open questions, and contribute to
a better understanding of this problem within the selected graph classes.
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