Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Competition Graphs of Jaco Graphs and the Introduction of the Grog
  Number of a Simple Connected Graph   Let $G^\rightarrow$ be a simple connected directed graph on $n \geq 2$
vertices and let $V^*$ be a non-empty subset of $V(G^\rightarrow)$ and denote
the undirected subgraph induced by $V^*$ by, $\langle V^* \rangle.$ We show
that the \emph{competition graph} of the Jaco graph $J_n(1), n \in \Bbb N, n
\geq 5,$ denoted by $C(J_n(1))$ is given by:\\ \\ $C(J_n(1)) = \langle V^*
\rangle_{V^* = \{v_i|3 \leq i \leq n-1\}} - \{v_iv_{m_i}| m_i = i +
d^+_{J_n(1)}(v_i), 3 \leq i \leq n-2\} \cup \{v_1, v_2, v_n\}.$\\ \\ Further to
the above, the concept of the \emph{grog number} $g(G^\rightarrow)$ of a simple
connected directed graph $G^\rightarrow$ on $n \geq 2$ vertices as well as the
general \emph{grog number} of the underlying graph $G$, will be introduced. The
\emph{grog number} measures the efficiency of an \emph{optimal predator-prey
strategy} if the simple directed graph models an ecological predator-prey
web.\\ \\ We also pose four open problems for exploratory research.

35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ