On \((a, d)\)-Antimagic Prisms

We deal with \((a, d)\)-antimagic labelings of the prisms.
A connected graph \(G = (V, E)\) is said to be \((a, d)\)-antimagic if there exist positive integers \(a, d\) and a bijection \(f: E \to \{1, 2, \ldots, |E|\}\) such that the induced mapping \(g_f: V \to {N}\), defined by \(g_f(v) = \sum \{f(u, v): (u, v) \in E(G)\}\), is injective and \(g_f(V) = \{a, a + d, \ldots, a + (|V| – 1)d\}\).

We characterize \((a, d)\)-antimagic prisms with even cycles and we conjecture that prisms with odd cycles of length \(n\), \(n \geq 7\), are \((\frac{n+7}{2}, 4)\)-antimagic.