On D-distance (anti)magic labelings of shadow graph of some graphs

Ngurah, Anak Agung Gede (Department of Civil Engineering, Universitas Merdeka Malang, Terusan Raya Dieng 62 -- 64 Malang, Indonesia)
Inayah, Nur (Department of Mathematics, Faculty of Science and Technology, State Islamic University Syarif Hidayatullah, Jl. Ir H. Juanda No. 95 Tangerang Selatan 15412, Indonesia.)
Musti, Mohamad Irvan Septiar (Department of Mathematics, Faculty of Science and Technology, State Islamic University Syarif Hidayatullah, Jl. Ir H. Juanda No. 95 Tangerang Selatan 15412, Indonesia.)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 12, No 1 (2024): Electronic Journal of Graph Theory and Applications

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}.