Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On k-resonant fullerene graphs   A fullerene graph $F$ is a 3-connected plane cubic graph with exactly 12
pentagons and the remaining hexagons. Let $M$ be a perfect matching of $F$. A
cycle $C$ of $F$ is $M$-alternating if the edges of $C$ appear alternately in
and off $M$. A set $\mathcal H$ of disjoint hexagons of $F$ is called a
resonant pattern (or sextet pattern) if $F$ has a perfect matching $M$ such
that all hexagons in $\mathcal H$ are $M$-alternating. A fullerene graph $F$ is
$k$-resonant if any $i$ ($0\leq i \leq k$) disjoint hexagons of $F$ form a
resonant pattern. In this paper, we prove that every hexagon of a fullerene
graph is resonant and all leapfrog fullerene graphs are 2-resonant. Further, we
show that a 3-resonant fullerene graph has at most 60 vertices and construct
all nine 3-resonant fullerene graphs, which are also $k$-resonant for every
integer $k>3$. Finally, sextet polynomials of the 3-resonant fullerene graphs
are computed.

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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: cs
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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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: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc