Inclusive distance antimagic graphs

Abstract

Let G be a nontrivial and connected graph of order n. Define a bijection function g : V(G) → {1, 2,…, n}. For any vertex v ∈ V(G), the neighbor sum g(v) + Σu∈N(v)g(u) is a called the weight of the vertices v, denoted by w(v). If w(x) ≠ w(y) for any two distinct vertices x and y, then g is called an inclusive distance antimagic labeling. In this paper, we present several results on inclusive distance antimagic labeling of graphs namely joint product, friendship, complete graph, path graph, cyle graph, star graph, doubel star, broom and wheel graph.