Determining which Fibonacci (p,r)(p,r)-cubes can be ZZ-transformation graphs

The Fibonacci (pp, rr)-cube is an interconnection topology, which includes a wide range of connection topologies as its special cases, such as the Fibonacci cube, the postal network, etc. Klavžar and Žigert [S. Klavžar, P. Žigert, Fibonacci cubes are the resonance graphs of fibonaccenes, Fibonacci Quart. 43 (2005) 269–276] proved that Fibonacci cubes are just the ZZ-transformation graphs (also called resonance graphs) of fibonaccenes, i.e. zigzag hexagonal chains. In this paper, we determine all Fibonacci (pp, rr)-cubes which can be the ZZ-transformation graphs of perfect matchings of plane (bipartite) graphs.