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 [Mathematical formula] 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 Ξ 2 (mod 4) with a few small exceptions. This result complements results by Kovár, Kovárová, and Krajc [P. Kovár, T.Kovárová, B. Krajc, On handicap labeling of regular graphs, manuscript, personal communication,2016] who found such graphs with regularities smaller than n - 7.