Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Brushing Number and Zero-Forcing Number of Graphs and their Line Graphs   In this paper we compare the brushing number of a graph with the zero-forcing
number of its line graph. We prove that the zero-forcing number of the line
graph is an upper bound for the brushing number by constructing a brush
configuration based on a zero-forcing set for the line graph. Using a similar
construction, we also prove the conjecture that the zero-forcing number of a
graph is no more than the zero-forcing number of its line graph; moreover we
prove that the brushing number of a graph is no more than the brushing number
of its line graph. All three bounds are shown to be tight.

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The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
4
The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex