  Let $G=(V,E)$ be a simple graph. A dominating set of $G$ is a subset
$D\subseteq V$ such that every vertex not in $D$ is adjacent to at least one
vertex in $D$. The cardinality of a smallest dominating set of $G$, denoted by
$\gamma(G)$, is the domination number of $G$. A dominating set $D$ is called a
secure dominating set of $G$, if for every $u\in V-D$, there exists a vertex
$v\in D$ such that $uv \in E$ and $D-\{v\}\cup\{u\}$ is a dominating set of
$G$. The cardinality of a smallest secure dominating set of $G$, denoted by
$\gamma_s(G)$, is the secure domination number of $G$. For any $k \in
\mathbb{N}$, the $k$-subdivision of $G$ is a simple graph $G^{\frac{1}{k}}$
which is constructed by replacing each edge of $G$ with a path of length $k$.
In this paper, we study the secure domination number of $k$-subdivision of $G$.
