The 3-domination-critical graphs with toughness one - Chen, Yaojun; Tian, Feng; Wei, Bing (Utilitas Mathematica, 2002)
A graph G is 3-domination-critical if its domination number γ is 3 and the addition of any edge decreases γ by 1. In this paper, we give a sufficient and necessary condition for a connected 3-domination-critical G to have toughness τ(G) = 1.