Regular handicap graphs of order n ≡ 4 (mod 8) - Dalibor Froncek; Aaron Shepanik (Electronic Journal of Graph Theory and Applications (EJGTA), 2022)
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, the weight w(xi) is the sum of labels of all neighbors of xi, and the sequence of the weights w(x1),w(x2),…,w(xn) forms an increasing arithmetic progression. A graph G is a handicap distance antimagic graph if it allows a handicap distance antimagic labeling. We construct r-regular handicap distance antimagic graphs of order n ≡ 4 (mod 8) for all feasible values of r.