Abstract
In this paper, we continue the study of the domination game in graphs introduced by Brešar et al. (SIAM J Discret Math 24:979–991, 2010). We study the total version of the domination game and show that these two versions differ significantly. We present a key lemma, known as the Total Continuation Principle, to compare the Dominator-start total domination game and the Staller-start total domination game. Relationships between the game total domination number and the total domination number, as well as between the game total domination number and the domination number, are established.
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