A note on the strength of a hypercube
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911081793847296 |
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| author | Huggan, Melissa A. Messinger, M. E. Pearson, Dylan |
| author_facet | Huggan, Melissa A. Messinger, M. E. Pearson, Dylan |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_21908 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on the strength of a hypercube Huggan, Melissa A. Messinger, M. E. Pearson, Dylan Combinatorics 05C78, 68R10 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. |
| title | A note on the strength of a hypercube |
| topic | Combinatorics 05C78, 68R10 |
| url | https://arxiv.org/abs/2507.21908 |