Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The total bondage number of grid graphs   The total domination number of a graph $G$ without isolated vertices is the
minimum number of vertices that dominate all vertices in $G$. The total bondage
number $b_t(G)$ of $G$ is the minimum number of edges whose removal enlarges
the total domination number. This paper considers grid graphs. An $(n,m)$-grid
graph $G_{n,m}$ is defined as the cartesian product of two paths $P_n$ and
$P_m$. This paper determines the exact values of $b_t(G_{n,2})$ and
$b_t(G_{n,3})$, and establishes some upper bounds of $b_t(G_{n,4})$.

17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph