Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algorithmic complexity of proper labeling problems   A proper labeling of a graph is an assignment of integers to some elements of
a graph, which may be the vertices, the edges, or both of them, such that we
obtain a proper vertex coloring via the labeling subject to some conditions.
The problem of proper labeling offers many variants and received a great
interest during recent years. We consider the algorithmic complexity of some
variants of the proper labeling problems, we present some polynomial time
algorithms and $ \mathbf{NP} $-completeness results for them.

24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn