A note on Distance Magic and Distance antimagic graphs

Abstract

Let G=(V,E) be a graph of order n. The graph G is said to be distance magic if there exists a bijection f:V(G)→{1,2,…,n} such that for all v∈V, w(v)=∑u∈N(v)f(u) is a constant, called vertex magic constant. The graph G is said to be distance anti-magic if w(u)≠w(v) for all u, v in G. We prove that several families of graphs are distance antimagic.