On Fibonacci (p,r) -cubes

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