# Get number of vertices when number of internal vertices is known ofr a full binary tree

But I can find a counter example:

      *
/   \
*     *
/ \   / \
*   * *   *


Here $k = 2$, but number of vertices is 6, and number of terminal vertices is 4.

Actually $k=3$ here, since the top of the tree is an internal node. That correctly gives $2\cdot 3+1=7$ total vertices, and $k+1=4$ external vertices (the lowest endpoints in the picture).