Fibonacci (p p , r r )-cubes which are median graphs ?
The Fibonacci (p p , r r )-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. Klavar, On median nature and enumerative properties of Fibonacci-like cubes, Discrete Math. 299 (2005) 145153]. The question for determining which Fibonacci (p p , r r )-cubes are median graphs is solved completely in this paper. We show that Fibonacci (p p , r r )-cubes are median graphs if and only if either r?p r ? p and r?2 r ? 2 , or p=1 p = 1 and r=n r = n .
fibonacci (p p median graph hypercube r r )-cube p p p p p r r r r r