The power of digraph products applied to labelings
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The ⊗h-product was introduced in 2008 by Figueroa-Centeno et al. as a way to construct new families of (super) edge-magic graphs and to prove that some of those families admit an exponential number of (super) edge-magic labelings. In this paper, we extend the use of the product ⊗h in order to study
the well know harmonious, sequential, partitional and (a, d)-edge antimagic total labelings. We prove that if a (p, q)-digraph with p ≤ q is harmonious and h : E(D) −→ Sn is any function, then und(D ⊗h Sn) is harmonious. We obtain analogous results for sequential and partitional labelings. We also prove that if G is a (super) (a, d)-edge-antimagic total tripartite graph, then nG is (super) (a ′ , d)-edge-antimagic total, where n ≥ 3, and d = 0, 2 and n is odd, or d = 1. We finish the paper providing an application of the product ⊗h to an arithmetic classical result when the function h is constant.