Some results on total domination in direct products of graphsDorbec, Paul (Avtor) Gravier, Sylvain (Avtor) Klavžar, Sandi (Avtor) Špacapan, Simon (Avtor) mathematicsgraph theorydirektni produkttotal domination▫$k$▫-tuple dominationopen packingdominationUpper and lower bounds on the total domination number of the direct product ofgraphs are given. The bounds involve the ▫$\{2\}$▫-total domination number, the total 2-tuple domination number, and the open packing number of the factors. Using these relationships one exact total domination number is obtained. An infinite family of graphs is constructed showing that the bounds are best possible. The domination number of direct products of graphs is also bounded from below.02017-03-31 14:30:51Članek v reviji65353sl