In this paper, it is pointed out that the definition of `Fibonacci \((p,r)\)-cube’ in many papers (denoted by \(I\Gamma_{n}^{(p,r)}\)) is incorrect. The graph \(I\Gamma_{n}^{(p,r)}\) is not the same as the original one (denoted by \(O\Gamma_{n}^{(p,r)}\)) introduced by Egiazarian and Astola. First, it is shown that \(I\Gamma_{n}^{(p,r)}\) and \(O\Gamma_{n}^{(p,r)}\) have different recursive structure. Then, it is proven that all the graphs \(O\Gamma_{n}^{(p,r)}\) are partial cubes. However, only a small part of graphs \(I\Gamma_{n}^{(p,r)}\) are partial cubes. It is also shown that \(I\Gamma_{n}^{(p,r)}\) and \(O\Gamma_{n}^{(p,r)}\) have different medianicity. Finally, several questions are listed for further investigation.