Regular handicap graphs of order n = 4 (mod 8)

A handicap distance antimagic labeling of a graph G = (V, E) with n vertices is a bijection (Formula presented): V {1, 2,…, n} with the property that f(x_i) = i, the weight w(x_i) 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.