A Remark on Total Domination Critical Graphs
Nader Jafari Rad, Sadegh Rahimi Sharebaf · 2008
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.