A new labeling construction from the⊗h-product

Abstract

The ⊗ h -product that refers 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 family of super edge-magic graphs with equal order and size. In this paper, we introduce a new labeling construction by changing the role of the factors. Using this new construction the range of applications grows up considerably. In particular, we can increase the information about magic sums of cycles and crowns.

(Di)graph Decompositions and Magic Type Labelings: A Dual Relation

“…All the results in the literature involving the ⊗ h -product had super edge-magic labeled digraphs in the second factor of the product. However, in [14] it was shown that other labeled (di)graphs can be used in order to enlarge the results obtained, showing that the ⊗ h -product is a very powerful tool. Next, we introduce the family T q σ of edge-magic labeled digraphs.…”

“…An edge-magic labeled digraph F is in T q σ if V (F ) = V , |E(F )| = q and the magic sum of the edge-magic labeling is equal to σ. Theorem 1.2. [14] Let D ∈ S k n and let h be any function h : E(D) → T q σ . Then D ⊗ h T q σ admits an edge-magic labeling with valence (p + q)(k…”