Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Family of Dense Mixed Graphs of Diameter $2$   A mixed graph is said to be dense if its order is close to the Moore bound
and it is optimal if there is not a mixed graph with the same parameters and
bigger order.
  We present a construction that provides dense mixed graphs of undirected
degree $q$, directed degree $\frac{q-1}{2}$ and order $2q^2$, for $q$ being an
odd prime power. Since the Moore bound for a mixed graph with these parameters
is equal to $\frac{9q^2-4q+3}{4}$ the defect of these mixed graphs is
$({\frac{q-2}{2}})^2-\frac{1}{4}$.
  In particular we obtain a known mixed Moore graph of order $18$, undirected
degree $3$ and directed degree $1$ called Bos\'ak's graph and a new mixed graph
of order $50$, undirected degree $5$ and directed degree $2$, which is proved
to be optimal.

16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph