Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Examples of distance magic labelings of the $6$-dimensional hypercube   A distance magic labeling of an $n$-dimensional hypercube is a labeling of
its vertices by natural numbers from $\{0, \ldots, 2^n-1\}$, such that for all
vertices $v$ the sum of the labels of the neighbors of $v$ is the same. Such a
labeling is called neighbor-balanced, if, moreover, for each vertex $v$ and an
index $i=0,\ldots,n-1$, exactly half of the neighbors of $v$ have digit $1$ at
$i$-th position of the binary representation of their label. We demonstrate
examples of non-neighbor-balanced distance magic labelings of $6$-dimensional
hypercube obtained by a SAT solver.

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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: cs
4
The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph