  Let $G$ be a finite, connected graph of order of at least 2, with vertex set
$V(G)$ and edge set $E (G)$. A set $S$ of vertices of the graph $G$ is a doubly
resolving set for $G$ if every two distinct vertices of $G$ are doubly resolved
by some two vertices of $S$. The minimal doubly resolving set of vertices of
graph $G$ is a doubly resolving set with minimum cardinality and is denoted by
$\psi(G)$. In this paper, first, we construct a class of graphs of order $2n+
\Sigma_{r=1}^{k-2}nm^{r}$, denoted by $LSG(n,m, k)$, and call these graphs as
the layer Sun graphs with parameters $n$, $m$ and $k$. Moreover, we compute
minimal doubly resolving sets and the strong metric dimension of layer Sun
graph $LSG(n,m, k)$ and the line graph of the layer Sun graph $LSG(n,m, k)$.
