Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum partial automorphisms of finite graphs   The partial automorphisms of a graph $X$ having $N$ vertices are the
bijections $\sigma:I\to J$ with $I,J\subset\{1,\ldots,N\}$ which leave
invariant the edges. These bijections form a semigroup $\widetilde{G}(X)$,
which contains the automorphism group $G(X)$. We discuss here the quantum
analogue of this construction, with a definition and basic theory for the
quantum semigroup of quantum partial automorphisms $\widetilde{G}^+(X)$, which
contains both $G(X)$, and the quantum automorphism group $G^+(X)$. We comment
as well on the case $N=\infty$, which is of particular interest, due to the
fact that $\widetilde{G}^+(X)$ is well-defined, while its subgroup $G^+(X)$,
not necessarily, at least with the currently known methods.

14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph