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

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.

Keywords


(a, d)-distance antimagic labeling; (a, d)-distance antimagic graph; 2-regular graph Math

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