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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Vira Hari Krisnawati
Department of Mathematics, University of Brawijaya, Malang, Indonesia
Electrical & Electronics Engineering

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On (a, d)-distance antimagic labeling of 2-regular graphs containing 6-cycles Muhammad Husnul Khuluq; Anak Agung Gede Ngurah; Noor Hidayat; Vira Hari Krisnawati
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 14, No 2 (2026): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

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Abstract

A graph G = (V(G), E(G)) of order n is called (a, d)-distance antimagic if there exists a bijection ℓ : V(G) → {1, 2, …, n} such that the set of vertex weights is {a, a + d, a + 2d, …, a + (n − 1)d}, where a > 0 and d ≥ 0. In such a case, ℓ is called an (a, d)-distance antimagic labeling of G. In this paper, we provide necessary and sufficient conditions of the graphs Cn ∪ tC6 where n ∈ {5, 7, 9, 11}, C2t+1 ∪ tC6, m(Cn ∪ C6), mCn ∪ ½(mn − 1)C6, and C10 ∪ mC3 ∪ tC6 to be (a, d)-distance antimagic for some positive integers m, n, and t.
Co-Authors Anak Agung Gede Ngurah Muhammad Husnul Khuluq Noor Hidayat