Let $\Delta$ be a connected Dynkin diagram attached to an indecomposable finite generalized Cartan matrix. Then $\Delta$ is of finite type if and only if it is isomorphic, as an oriented labelled Dynkin diagram, to exactly one diagram in the list
Here $B_n$ and $C_n$ denote the two possible orientations of the unique double edge in the corresponding non-simply-laced chain, and $G_2$ denotes the rank-two diagram with a triple edge. Conversely, each diagram in the displayed list is of finite type.