Minimal graph in which the intersection of two longest paths is not a separator

We prove that for a connected simple graph $G$ with $n\le 10$ vertices, and two longest paths $C$ and $D$ in $G$, the intersection of vertex sets $V©\cap V(D)$isaseparator\mathrm{.}Thisshowsthatthegraphfoundpreviouslywith$n=11$, in which the complement of the intersection of vertex sets $V(C)\cap V(D)$ of two longest paths is connected, is minimal.