On regular handicap graphs of order n 0 mod 8 - Dalibor Froncek; Aaron Shepanik (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2018)
A handicap distance antimagic labeling of a graph G = (V, E) with n vertices is a bijection f̂ : V → 1, 2, …, n with the property that f̂(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 0 8 for all feasible values of r.