Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relating the total domination number and the annihilation number for
  quasi-trees and some composite graphs   The total domination number $\gamma_{t}(G)$ of a graph $G$ is the cardinality
of a smallest set $D\subseteq V(G)$ such that each vertex of $G$ has a neighbor
in $D$. The annihilation number $a(G)$ of $G$ is the largest integer $k$ such
that there exist $k$ different vertices in $G$ with the degree sum at most
$m(G)$. It is conjectured that $\gamma_{t}(G)\leq a(G)+1$ holds for every
nontrivial connected graph $G$. The conjecture has been proved for graphs with
minimum degree at least $3$, trees, certain tree-like graphs, block graphs, and
cactus graphs. In the main result of this paper it is proved that the
conjecture holds for quasi-trees. The conjecture is verified also for some
graph constructions including bijection graphs, Mycielskians, and the newly
introduced universally-identifying graphs.

7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex