A note on sequences variant of irregularity strength for hypercubes

Let f: E ↦ \1,2,,k\ be an edge coloring of the n - dimensional 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 i - dimensional edge incident to v. In the 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.