Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Jacobsthal numbers in generalised Petersen graphs   We prove that the number of $1$-factorisations of a generalised Petersen
graph of the type $GP(3k,k)$ is equal to the $k$th Jacobsthal number $J(k)$ if
$k$ is odd, and equal to $4J(k)$, when $k$ is even. Moreover, we verify the
list colouring conjecture for $GP(3k,k)$.

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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: cs