A new labeling construction from the $\otimes_h$-product

TL;DR

This paper introduces a new labeling construction based on the $ imes_h$-product, expanding the applications of graph labelings, especially for cycles and crowns, beyond previous limitations.

Contribution

It presents a novel construction method that alters the role of factors in the $ imes_h$-product, broadening the scope of graph labeling applications.

Findings

Enhanced understanding of magic sums in cycles and crowns.

Broader applicability of labeling techniques using the new construction.

Increased range of applications for the $ imes_h$-product in graph theory.

Abstract

The $\otimes_h$-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.