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 f : 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 x i , and the sequence of the weights w ( x 1 ), w ( x 2 ), …, 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 .