The diameter of total domination and independent domination vertex-critical graphs
Michelle Edwards, Gary MacGillivray · Australas. J Comb. · 2012
We show that the diameter of a total domination vertex-critical graph is at most 5(γt − 1)/3, and that the diameter of an independent domination vertex-critical graph is at most 2(i − 1). For all values of γt ≡ 2( mod 3) there exists a total domination vertex-critical graph with the maximum possible diameter. For all values of i ≥ 2 there exists an independent domination vertex-critical graph with the maximum possible diameter.