A note on the strength of a hypercube

TL;DR

This paper improves the upper bound on the strength of a hypercube graph, a measure related to vertex labelings and graph properties, extending the understanding of hypercube graph characteristics.

Contribution

It provides a tighter upper bound for the strength of hypercube graphs, advancing the theoretical understanding of graph strength measures.

Findings

Improved upper bound for hypercube strength

Enhanced understanding of graph labeling properties

Contributes to graph theory bounds

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 $f$ of graph $G$, the strength of $f$ is the maximum sum of the labels on any pair of adjacent vertices. The strength of $G$ is defined as the minimum strength of $f$, taken over all vertex orderings of $G$. The strength of the hypercube is unknown, but bounded. In this note, we provide an improved upper bound for the strength of a hypercube.