A graph is called gamma-critical if the removal of any vertex from the graph decreases the domination number, while a graph with no isolated vertexis gamma(t)-critical if the removal of any vertex that is not adjacent to a vertex of degree 1 decreases the total domination number. A gamma(t)-critical graph that has total domination number k, is called k-gamma(t)-critical. In this paper, we introduce a class of k-gamma(t)-critical graphs of high connectivity for each integer k >= 3. In particular, we provide a partial answer to the question "Which graphs are gamma-critical and gamma(t)-critical or one but not the other?" posed in a recent work [W. Goddard, T.W. Haynes, M.A. Henning, L.C. van der Merwe, The diameter of total domination vertex critical graphs, Discrete Math. 286 (2004) 255-261].
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机译：如果从图中删除任何一个顶点会减少控制数，则该图称为“γ临界”，而在没有孤立顶点的情况下，如果不与度为1的顶点相邻的任何顶点的去除，则该图称为γ（t）临界。减少总控制数。具有总支配数k的gamma（t）临界图称为k-gamma（t）临界。在本文中，我们针对每个k> = 3的整数介绍了一类具有高连通性的k-gamma（t）临界图。特别是，我们对“哪个图是gamma临界和gamma（ t）是关键的，还是其中一个而不是另一个？”摆在最近的工作[W. T.W.哥达德Haynes，M.A. Henning，L.C. van der Merwe，总支配顶点临界图的直径，离散数学。 286（2004）255-261]。
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