A note on sequences variant of irregularity strength for hypercubes

Anna Flaszczyńska, Aleksandra Gorzkowska and Mariusz Woźniak

Applied Mathematics and Computation, 2025, vol. 495, issue C

Abstract: Let f:E→{1,2,…,k} be an edge-coloring of the n-dimension hypercube Hn. By the palette at a vertex v we mean the sequence (f(e1(v)),f(e1(v)),…,f(en(v))), where ei(v) is the edge incident to v that connects vertices differing in the ith element. In this paper, we show that two colors are enough to distinguish all vertices of the n-dimensional hypercube Hn (n≥2) by their palettes. We also show that if f is a proper edge-coloring of the hypercube Hn (n≥5), then n colors suffice to distinguish all vertices by their palettes.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:495:y:2025:i:c:s0096300325000396

DOI: 10.1016/j.amc.2025.129312

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