Let $(R, \mathfrak m)$ be a complete local normal domain of dimension $2$ with residue field $R/\mathfrak m$ algebraically closed and characteristic $0$. Assume Spec$(R)$ has rational singularity, let $\pi: X \to \text{Spec}(R)$ be minimal resolution of singularities with exceptional divisor $E=\pi^{-1}(\mathfrak m)$. If $E$ has exactly one irreducible component, then must it be true that $R$ is a cyclic quotient singularity?