On D-distance (anti)magic labelings of shadow graph of some graphs - Ngurah, Anak Agung Gede; Inayah, Nur; Musti, Mohamad Irvan Septiar (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2024)
Let G be a graph with vertex set V(G) and diameter diam(G). Let D ⊆ 0, 1, 2, 3, …, diam(G) and φ : V(G)→1, 2, 3, …, |V(G)| be a bijection. The graph G is called D-distance magic, if s ∈ ND(t)φ(s) is a constant for any vertex t ∈ V(G). The graph G is called (α, β)-D-distance antimagic, if s ∈ ND(t)φ(s):t ∈ V(G) is a set α, α + β, α + 2β, …, α + (|V(G)| − 1)β. In this paper, we study D-distance (anti)magic labelings of shadow graphs for D = 1, 0, 1, 2, and 0, 2.