Tight Upper Bounds for the Domination Numbers of Graphs With Given Order and Minimum Degree

Let γ(n, δ) denote the maximum possible domination number of a graph with n vertices and minimum degree δ. Using known results we determine γ(n, δ) for δ = 0, 1, 2, 3, n ≥ δ +1 and for all n, δ where δ = n − k and n is sufficiently large relative to k. We also obtain γ(n, δ) for all remaining values of (n, δ) when n ≤ 14 and all but 6 values of (n, δ) when n = 15 or 16.