Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Super edge-magic deficiency of join-product graphs   A graph $G$ is called \textit{super edge-magic} if there exists a bijective
function $f$ from $V(G) \cup E(G)$ to $\{1, 2, \ldots, |V(G) \cup E(G)|\}$ such
that $f(V(G)) = \{1, 2, \ldots, |V(G)|\}$ and $f(x) + f(xy) + f(y)$ is a
constant $k$ for every edge $xy$ of $G$. Furthermore, the \textit{super
edge-magic deficiency} of a graph $G$ is either the minimum nonnegative integer
$n$ such that $G \cup nK_1$ is super edge-magic or $+\infty$ if there exists no
such integer.
  \emph{Join product} of two graphs is their graph union with additional edges
that connect all vertices of the first graph to each vertex of the second
graph. In this paper, we study the super edge-magic deficiencies of a wheel
minus an edge and join products of a path, a star, and a cycle, respectively,
with isolated vertices.

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The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg