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| Paper IPM / M / 8440 |
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| Abstract: | |
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A graph G with no isolated vertex is total domination vertex
critical if for any vertex v of G that is not adjacent to a
vertex of degree one, the total domination number of G − v is
less than the total domination number of G. These graphs we call
γt-critical. If such a graph G has total domination
number k, we call it k−γt-critical. We verify an open
problem of k−γt-critical graphs and obtain some results on
the characterization of total domination critical graphs of order
n = ∆(G)(γt(G) − 1) + 1.
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