Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two cycle-chord graphs are $e$-positive   We prove Gebhard and Sagan's $(e)$-positivity of the line graphs of tadpoles
in noncommuting variables. This implies the $e$-positivity of these line
graphs. We then extend this $(e)$-positivity result to that of certain
cycle-chord graphs, and derive the bivariate generating function of all
cycle-chord graphs.

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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
3
The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg