Distance Antimagic Graphs

Let \( G = (V, E) \) be a graph of order \( n \). Let \( f: V \to \{1, 2, \dots, n\} \) be a bijection. For any vertex \( v \in V \), the neighbor sum \( \sum_{u \in N(v)} f(u) \) is called the weight of the vertex \( v \) and is denoted by \( w(v) \). If \( w(x) \neq w(y) \) for any two distinct vertices \( x \) and \( y \), then \( f \) is called a distance antimagic labeling. In this paper, we present several results on distance antimagic graphs along with open problems and conjectures.