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

Anak Agung Gede Ngurah, Nur Inayah, Mohamad Irvan Septiar Musti


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}.


D-distance (anti)magic labeling, D-distance (anti)magic graph, shadow graph

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DOI: http://dx.doi.org/10.5614/ejgta.2024.12.1.3


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