Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Connectivity of some Algebraically Defined Digraphs   Let $p$ be a prime, $e$ a positive integer, $q = p^e$, and let $\mathbb{F}_q$
denote the finite field of $q$ elements. Let $f_i :
\mathbb{F}_q^2\to\mathbb{F}_q$ be arbitrary functions, where $1\le i\le l$, $i$
and $l$ are integers. The digraph $D = D(q;\bf{f})$, where ${\bf
f}=(f_1,\dotso,f_l) : \mathbb{F}_q^2\to\mathbb{F}_q^l$, is defined as follows.
The vertex set of $D$ is $\mathbb{F}_q^{l+1}$. There is an arc from a vertex
${\bf x} = (x_1,\dotso,x_{l+1})$ to a vertex ${\bf y} = (y_1,\dotso,y_{l+1})$
if $ x_i + y_i = f_{i-1}(x_1,y_1) $ for all $i$, $2\le i \le l+1$. In this
paper we study the strong connectivity of $D$ and completely describe its
strong components. The digraphs $D$ are directed analogues of some
algebraically defined graphs, which have been studied extensively and have many
applications.

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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
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The categories of this paper are: econ
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th