(Ars Combinatoria, 164, 33-55, 2025) Almeida, Maurice; De Sa, Kingel Savia
Let G = (V, E) be a graph of order n without isolated vertices. A bijection f: V → {1, 2, . . . , n} is called a local distance antimagic labeling, if w(u) ̸= w(v) for every edge uv of G, where w(u) = P x∈N(u) f(x). The local distance antimagic chromatic number χld(G) is de ned to be the minimum number of colors taken over all colorings of G induced by local distance antimagic labelings of G. The concept of Generalized Mycielskian graphs was introduced by Stiebitz [20]. In this paper, we study the local distance antimagic labeling of the Generalized Mycielskian graphs.