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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Pancahayani, Sigit
Doctoral Program in Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung, Indonesia
Electrical & Electronics Engineering

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Magic labeling on graphs with ascending subgraph decomposition Pancahayani, Sigit; Simanjuntak, Rinovia; Uttunggadewa, Saladin
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 12, No 2 (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.2024.12.2.4

Abstract

Let t and q be positive integers that satisfy C(t + 1,2) ≤ q < C(t + 2,2) and let G be a simple and finite graph of size q. G is said to have ascending subgraph decomposition (ASD) if G can be decomposed into t subgraphs H1,H2,…,Ht without isolated vertices such that Hi is isomorphic to a proper subgraph of Hi+1 for 1 ≤ i ≤ t - 1, where {E(H1),…,E(Ht)} is a partition of E(G). A graph that admits an ascending subgraph decomposition is called an ASD graph.In this paper, we introduce a new type of magic labeling based on the notion of ASD. Let G be an ASD graph and f : V (G) ∪E(G) →{1,2,…,|V (G)| + |E(G)|} be a bijection. The weight of a subgraph Hi (1 ≤ i ≤ n) is w(Hi) = ∑ v∈V (Hi)f(v) + ∑ e∈E(Hi)f(e). If the weight of each ascending subgraph is constant, say w(Hi) = k, ∀ 1 ≤ i ≤ t, then f is called an ASD-magic labeling of G and G is called an ASD-magic graph. We present general properties of ASD-magic graphs and characterize certain classes of them.
Co-Authors Simanjuntak, Rinovia Uttunggadewa, Saladin