Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimal Zero Forcing Sets   In this paper, we study minimal (with respect to inclusion) zero forcing
sets. We first investigate when a graph can have polynomially or exponentially
many distinct minimal zero forcing sets. We also study the maximum size of a
minimal zero forcing set $\overline{\operatorname{Z}}(G)$, and relate it to the
zero forcing number $\operatorname{Z}(G)$. Surprisingly, we show that the
equality $\overline{\operatorname{Z}}(G)=\operatorname{Z}(G)$ is preserved by
deleting a universal vertex, but not by adding a universal vertex. We also
characterize graphs with extreme values of $\overline{\operatorname{Z}}(G)$ and
explore the gap between $\overline{\operatorname{Z}}(G)$ and
$\operatorname{Z}(G)$.

29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga