2018/02/28 by Benjamin J. Ellis, David A. Nash, Ellis, Benjamin +5
Computer Science · Engineering · #05B25 #05C65 #05C78 #51A99 #Combinatorics (math.CO) #Digital Image Processing Techniques #FOS: Mathematics #Graph Labeling and Dimension Problems #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1802.10392
openalex publication_date 2018/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article studies a generalization of magic squares to k-uniform hypergraphs. In traditional magic squares the entries come from the natural numbers. A magic labeling of the vertices in a graph or hypergraph has since been generalized to allow for labels coming from any abelian group. We demonstrate an algorithm for determining whether a given hypergraph has a magic labeling over some abelian group. A slight adjustment of this algorithm also allows one to determine whether a given hypergraph can be magically labeled over ℤ. As a demonstration, we use these algorithms to determine the number of magic n3-configurations for n=7, …, 14.