On (a, d)-distance antimagic labeling of 2-regular graphs containing 6-cycles

Muhammad Husnul Khuluq (Department of Mathematics, University of Brawijaya, Malang)
Anak Agung Gede Ngurah (Universitas Merdeka Malang)
Noor Hidayat (Department of Mathematics, University of Brawijaya, Malang)
Vira Hari Krisnawati (Department of Mathematics, University of Brawijaya, Malang, Indonesia)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 14, No 2 (2026): Electronic Journal of Graph Theory and Applications

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.