Regular Handicap Graphs of Odd Order

A handicap distance antimagic labeling of a graph \(G = (V,E)\) with \(n\) vertices is a bijection \(f : V \to \{1,2,\dots,n\}\) with the property that \(f(x_i) = i\) and the sequence of the weights \(w(x_1), w(x_2), \dots, w(x_n)\) (where \(w(x_i) = \sum_{x_j \in N(x_i)}{f(x_j)}\)) forms an increasing arithmetic progression. A graph \(G\) is a handicap distance antimagic graph if it allows a handicap distance antimagic labeling.

We construct regular handicap distance antimagic graphs for every feasible odd order.