  Let $G=(V(G),E(G))$ be a simple graph. A restrained double Roman dominating
function (RDRD-function) of $G$ is a function $f: V(G) \rightarrow \{0,1,2,3\}$
satisfying the following properties: if $f(v)=0$, then the vertex $v$ has at
least two neighbours assigned 2 under $f$ or one neighbour $u$ with $f(u)=3$;
and if $f(v)=1$, then the vertex $v$ must have one neighbor $u$ with $f(u) \geq
2$; the induced graph by vertices assigned 0 under $f$ contains no isolated
vertex. The weight of a RDRD-function $f$ is the sum $f(V)=\sum_{v \in V(G)}
f(v)$, and the minimum weight of a RDRD-function on $G$ is the restrained
double Roman domination number (RDRD-number) of $G$, denoted by
$\gamma_{rdR}(G)$. In this paper, we first prove that the problem of computing
RDRD-number is NP-hard even for chordal graphs. And then we study the impact of
some graph operations, such as strong product, cardinal product and corona with
a graph, on restrained double Roman domination number.
