Regular handicap tournaments of high degree

A 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(xi) = i and the sequence of the weights w(x1), w(x2), . . . , w(xn) (where w(xi) = ∑ xj∈N(xi) f(xj)) forms an increasing arithmetic progression with difference one. A graph G is a handicap distance antimagic graph if it allows a handicap distance antimagic labeling. We construct (n− 7)-regular handicap distance antimagic graphs for every order n ≡ 2 (mod 4) with a few small exceptions. This result complements results by Kovář, Kovářová, and Krajc [P. Kovář, T. Kovářová, B. Krajc, On handicap labeling of regular graphs, manuscript, personal communication, 2016] who found such graphs with regularities smaller than n− 7.