English

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 ff of graph GG, the strength of ff is the maximum sum of the labels on any pair of adjacent vertices. The strength of GG is defined as the minimum strength of ff, taken over all vertex orderings of GG. 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

R2 v1 2026-07-01T04:24:15.060Z