Total domination critical graphs with maximal order
Fan Li, Mei Lu · Scientia Sinica Mathematica · 2011
A graph G without isolated vertices is total domination vertex critical, if for any vertex v of G that is not adjacent to a pendant vertex, the total domination number of G - v is less than the total domination number of G. We call these graphs γt-critical. If G is a γt-critical graph of order n, then it can be shown that n ≤ Δ(G)(γt(G) - 1) + 1, where Δ(G) is the maximum degree of G. In this paper, we characterize the graphs in the case n = Δ(G)(γt(G) - 1) + 1 with γt(G) = 3.