A note on the strength of a hypercube
Combinatorics
2025-07-30 v1
Abstract
As a generalization of super magic strength, the strength of a graph was introduced in [R. Ichishima, F.A. Muntaner-Batle, A. Oshima, Bounds for the strength of graphs, Austral. J. of Combin. 72(3) (2018) 492-508]. For a vertex ordering of graph , the strength of is the maximum sum of the labels on any pair of adjacent vertices. The strength of is defined as the minimum strength of , taken over all vertex orderings of . The strength of the hypercube is unknown, but bounded. In this note, we provide an improved upper bound for the strength of a hypercube.
Keywords
Cite
@article{arxiv.2507.21908,
title = {A note on the strength of a hypercube},
author = {Melissa A. Huggan and M. E. Messinger and Dylan Pearson},
journal= {arXiv preprint arXiv:2507.21908},
year = {2025}
}
Comments
12 pages, 2 tables