On 4-γ t -Critical Graphs of Order 4+Δ (G)
Mehdi Hassankhani, Nader Jafari Rad · 2007
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 total domination critical or just γt-critical. If such a graph G has total domination number k, we call it k-γt-critical. We study an open problem of k-γt-critical graphs and obtain some results on the characterization of total domination critical graphs of order Δ(G)+4. Mathematics Subject Classification: 05C69