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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
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.
Electrical & Electronics Engineering

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On D-distance (anti)magic labelings of shadow graph of some graphs Ngurah, Anak Agung Gede; Inayah, Nur; Musti, Mohamad Irvan Septiar
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 12, No 1 (2024): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2024.12.1.3

Abstract

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}.
Co-Authors Ngurah, Anak Agung Gede Nur Inayah