Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nontrivial nuciferous graphs exist   A nuciferous graph is a simple graph with a non-singular $0$-$1$ adjacency
matrix $A$ such that all the diagonal entries of $A^{-1}$ are zero and all the
off-diagonal entries of $A^{-1}$ are non-zero. Sciriha et al. conjectured that
except $K_2$, no nuciferous graph exists. We disprove this conjecture.
Moreover, we conjecture that there infinitely many nuciferous Cayley graphs.

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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg