  Let $G$ be a connected graph and $d(a,b)$ be the distance between the
vertices $a$ and $b$. A subset $U =\{u_1,u_2,\cdots,u_k\}$ of the vertices is
called a resolving set for $G$ if for every two distinct vertices $a,b \in
V(G)$, there is a vertex $u_\xi \in U$ such that $d(a,u_\xi)\neq d(b,u_\xi)$. A
resolving set containing a minimum number of vertices is called a metric basis
for $G$ and the number of vertices in a metric basis is its metric dimension
denoted by $dim(G)$. A resolving set $U$ for $G$ is fault-tolerant if $U
\setminus \{u\}$ is also a resolving set, for each $u \in U$, and the
fault-tolerant metric dimension of $G$ is the minimum cardinality of such a
set. In this paper we introduce the study of the fault-tolerant metric
dimension of $P(n,2)$ with prism graph.
