Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Contemplating on Brush Numbers of Mycielski Jaco Graphs, $\mu(J_n(1)), n
  \in \Bbb N$   The concept of the brush number $b_r(G)$ was introduced for a simple
connected undirected graph $G$. The concept will be applied to the Mycielski
Jaco graph $\mu(J_n(1)), n \in \Bbb N,$ in respect of an \emph{optimal
orientation} of $J_n(1)$ associated with $b_r(J_n(1)).$ Further for the
aforesaid, the concept of a \emph{brush centre} of a simple connected graph
will be introduced. Because brushes themselves may be technology of kind, the
technology in real world application will normally be the subject of
maintenance or calibration or virus vetting or alike. Finding a \emph{brush
centre} of a graph will allow for well located maintenance centres of the
brushes prior to a next cycle of cleaning.

20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th