Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quasi-total Roman domination in graphs   A quasi-total Roman dominating function on a graph $G=(V, E)$ is a function
$f : V \rightarrow \{0,1,2\}$ satisfying the following:
  - every vertex $u$ for which $f(u) = 0$ is adjacent to at least one vertex
$v$ for which $f(v) =2$, and
  - if $x$ is an isolated vertex in the subgraph induced by the set of vertices
labeled with 1 and 2, then $f(x)=1$.
  The weight of a quasi-total Roman dominating function is the value
$\omega(f)=f(V)=\sum_{u\in V} f(u)$. The minimum weight of a quasi-total Roman
dominating function on a graph $G$ is called the quasi-total Roman domination
number of $G$. We introduce the quasi-total Roman domination number of graphs
in this article, and begin the study of its combinatorial and computational
properties.

13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex