A note on incomplete regular tournaments with handicap two of order n ≡ 8 (mod 16)

A d-handicap distance antimagic labeling of a graph G = (V, E) with n vertices is a bijection f : V → {1, 2, . . . , n} with the property that f(x_i) = i and the sequence of weights w(x₁), w(x₂), . . . , w(x_n) (where w(x_i) = ∑_xixj∈E f(x_j)) forms an increasing arithmetic progression with common difference d. A graph G is a d-handicap distance antimagic graph if it allows a d-handicap distance antimagic labeling. We construct a class of k-regular 2-handicap distance antimagic graphs for every order n ≡ 8 (mod 16), n ≥ 56 and 6 ≤ k ≤ n - 50.