Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new application of the $\otimes_h$-product to $\alpha$-labelings   The weak tensor product was introduced by Snevily as a way to construct new
graphs that admit $\alpha$-labelings from a pair of known $\alpha$-graphs. In
this article, we show that this product and the application to
$\alpha$-labelings can be generalized by considering as a second factor of the
product, a family $\Gamma$ of bipartite $(p,q)$-graphs, $p$ and $q$ fixed. The
only additional restriction that we should consider is that for every $F\in
\Gamma$, there exists and $\alpha$-labeling $f_F$ with $f_F(V(F))=L\cup H$,
where $L,H \subset [0,q]$ are the stable sets induced by the characteristic of
$f_F$ and they do not depend on $F$. We also obtain analogous applications to
near $\alpha$-labelings and bigraceful labelings.

30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph