Regular graphs are antimagic

An undirected simple graph G = (V, E) is called antimagic if there exists an injective function f : E -> {1,...,vertical bar E vertical bar} such that Sigma(e is an element of E(u)) f(e) not equal Sigma(e is an element of E(v)) f(e) for any pair of different nodes u, v is an element of V. In this note we prove - with a slight modification of an argument of Cranston et al. - that k-regular graphs are antimagic for k >= 2.