Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Realization of digraphs in Abelian groups and its consequences   Let $\overrightarrow{G}$ be a directed graph with no component of orderless
than~$3$, and let $\Gamma$ be a finite Abelian group such that
  $|\Gamma|\geq 4|V(\overrightarrow{G})|$ or if $|V(\overrightarrow{G})|$ is
large enough with respect to an arbitrarily fixed $\varepsilon>0$ then
  $|\Gamma|\geq (1+\varepsilon)|V(\overrightarrow{G})|$. We show that there
exists an injective mapping $\varphi$ from $V(\overrightarrow{G})$ to the group
$\Gamma$ such that $\sum_{x\in V(C)}\varphi(x) = 0$ for every connected
component $C$ of $\overrightarrow{G}$, where $0$ is the identity element of
$\Gamma$. Moreover we show some applications of this result to group distance
magic labelings.

19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol