Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Total domination polynomial of graphs from primary subgraphs   Let $G = (V, E)$ be a simple graph of order $n$. The total dominating set is
a subset $D$ of $V$ that every vertex of $V$ is adjacent to some vertices of
$D$. The total domination number of $G$ is equal to minimum cardinality of
total dominating set in $G$ and denoted by $\gamma_t(G)$. The total domination
polynomial of $G$ is the polynomial $D_t(G,x)=\sum d_t(G,i)$, where $d_t(G,i)$
is the number of total dominating sets of $G$ of size $i$. Let $G$ be a
connected graph constructed from pairwise disjoint connected graphs $G_1,\ldots
,G_k$ by selecting a vertex of $G_1$, a vertex of $G_2$, and identify these two
vertices. Then continue in this manner inductively. We say that $G$ is obtained
by point-attaching from $G_1, \ldots ,G_k$ and that $G_i$'s are the primary
subgraphs of $G$. In this paper, we consider some particular cases of these
graphs that most of them are of importance in chemistry and study their total
domination polynomials.

34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys