Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On $k$-rainbow independent domination in graphs   In this paper, we define a new domination invariant on a graph $G$, which
coincides with the ordinary independent domination number of the generalized
prism $G \Box K_k$, called the $k$-rainbow independent domination number and
denoted by $\gamma_{{\rm ri}k}(G)$. Some bounds and exact values concerning
this domination concept are determined. As a main result, we prove a
Nordhaus-Gaddum-type theorem on the sum for $2$-rainbow independent domination
number, and show if G is a graph of order $n \geq 3$, then $5\leq \gamma_{{\rm
ri}2}(G)+\gamma_{{\rm ri}2}(\overline{G})\leq n+3$, with both bounds being
sharp.

1
The categories of this paper are: cs
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
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
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th