Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An explicit formula for obtaining $(q+1,8)$-cages and others small
  regular graphs of girth 8   Let $q$ be a prime power; $(q+1,8)$-cages have been constructed as incidence
graphs of a non-degenerate quadric surface in projective 4-space $P(4, q)$. The
first contribution of this paper is a construction of these graphs in an
alternative way by means of an explicit formula using graphical terminology.
Furthermore by removing some specific perfect dominating sets from a
$(q+1,8)$-cage we derive $k$-regular graphs of girth 8 for $k= q-1$ and $k=q$,
having the smallest number of vertices known so far.

16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th