Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Edge-girth-regular graphs arising from biaffine planes and Suzuki groups   An edge-girth-regular graph $egr(v,k,g,\lambda)$, is a $k$-regular graph of
order $v$, girth $g$ and with the property that each of its edges is contained
in exactly $\lambda$ distinct $g$-cycles. An $egr(v,k,g,\lambda)$ is called
extremal for the triple $(k,g,\lambda)$ if $v$ is the smallest order of any
$egr(v,k,g,\lambda)$.
  In this paper, we introduce two families of edge-girth-regular graphs. The
first one is a family of extremal $egr(2q^2,q,6,(q-1)^2(q-2))$ for any prime
power $q\geq 3$ and, the second one is a family of $egr(q(q^2+1),q,5,\lambda)$
for $\lambda\geq q-1$ and $q\geq 8$ an odd power of $2$. In particular, if
$q=8$ we have that $\lambda=q-1$.

23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics