A Remark on Total Domination Critical Graphs
نویسنده
چکیده
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. We call these graphs γt-critical. In this paper, we disprove a conjecture posed in a recent paper(On an open problem concerning total domination critical graphs, Expo. Math. 25 (2007), 175-179). Mathematics Subject Classification: 05C69.
منابع مشابه
On the diameter of total domination vertex critical graphs
In this paper, we consider various types of domination vertex critical graphs, including total domination vertex critical graphs and independent domination vertex critical graphs and connected domination vertex critical graphs. We provide upper bounds on the diameter of them, two of which are sharp. MSC (2010): 05C12, 05C69
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