  Let $G=(V,E)$ be a finite connected simple graph with vertex set $V$ and edge
set $E$. A signed Roman dominating function (SRDF) on a graph $G$ is a function
$f: V \rightarrow \{-1, 1, 2\}$ that satisfies two conditions: (i) $\sum_{y\in
N[x]} f(y)\geq1$ for each $x\in V$, where the set $N[x]$ is the closed
neighborhood of $x$ consisting of $x$ and vertices of $V$ that are adjacent to
$x$, and (ii) each vertex $x\in V$ where $f(x) = -1$ is adjacent to at least
one vertex $y\in V$ where $f(y)=2$. The weight of a SRDF is the sum of its
function values over all vertices. The signed Roman domination number of $G$,
denoted by $\gamma_{SR}(G)$, is the minimum weight of a SRDF on $G$. In this
paper, we investigate the signed Roman domination number of the Ladder graph
$LG_n$, the circular Ladder graph $CL_n$ and their complements.
