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.
Is part ofDiscrete Mathematics, 2012, vol. 312, num. 2, p. 221-228
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López Masip, Susana-Clara; Muntaner Batle, F. A.; Rius Font, Miquel (Elsevier, 2013)In this paper we study the edge-magicness of graphs with equal size and order, and we use such graphs and digraph products in order to construct labelings of different classes and of different graphs. We also study super ...
López Masip, Susana-Clara; Muntaner Batle, F. A.; Prabu, M. (Elsevier, 2017)The -product that is referred in the title was introduced in 2008 as a generalization of the Kronecker product of digraphs. Many relations among labelings have been obtained since then, always using as a second factor a ...
López Masip, Susana-Clara (Elsevier, 2017)Gallian's survey shows that there is a big variety of labelings of graphs. By means of (di)graphs products we can establish strong relations among some of them. Moreover, due to the freedom of one of the factors, we can ...