Fibonacci (pp, rr)-cubes which are median graphs

The Fibonacci (pp, rr)-cube is an interconnection topology, which unifies a wide range of connection topologies, such as hypercube, Fibonacci cube, postal network, etc. It is known that the Fibonacci cubes are median graphs [S. Klavžar, On median nature and enumerative properties of Fibonacci-like cubes, Discrete Math. 299 (2005) 145–153]. The question for determining which Fibonacci (pp, rr)-cubes are median graphs is solved completely in this paper. We show that Fibonacci (pp, rr)-cubes are median graphs if and only if either r≤pr≤p and r≤2r≤2, or p=1p=1 and r=nr=n.