Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fullerene graphs of small diameter   A fullerene graph is a cubic bridgeless plane graph with only pentagonal and
hexagonal faces. We exhibit an infinite family of fullerene graphs of diameter
$\sqrt{4n/3}$, where $n$ is the number of vertices. This disproves a conjecture
of Andova and \v{S}krekovski [MATCH Commun. Math. Comput. Chem. 70 (2013)
205-220], who conjectured that every fullerene graph on $n$ vertices has
diameter at least $\lfloor \sqrt{5n/3}\rfloor-1$.

12
The categories of this paper are: nucl-th
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The categories of this paper are: stat
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
5
The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
23
The categories of this paper are: solv-int