On regular handicap graphs of order $n \equiv 0$ mod 8

Abstract

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(x_i) = i, the weight w(x_i) is the sum of labels of all neighbors of x_i, and the sequence of the weights w(x₁), w(x₂), …, w(x_n) 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 $n \equiv 0 \pmod{8}$ for all feasible values of r.