Distance antimagic labeling of join and corona of two graphs

Abstract

Let G be a graph of order n. Let f:V(G)⟶{1,2,…,n} be a bijection. The weight wf(v) of a vertex v with respect to f is defined by wf(v)=∑x∈N(v)f(x), where N(v) is the open neighborhood of v. The labeling f is said to be distance antimagic if wf(u)≠wf(v) for every pair of distinct vertices u,v∈V(G). If the graph G admits such a labeling, then G is said to be a distance antimagic graph. In this paper we investigate the existence of distance antimagic labelings of G+H and G∘H.