Note: Fibonacci (p, r)-cubes which are median graphs

Authors:
Lifeng Ou;Heping Zhang
Affiliations:
School of Mathematics and Computer Science Institute, Northwest University for Nationalities, Lanzhou, Gansu 730030, People's Republic of China;School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People's Republic of China
Venue:
Discrete Applied Mathematics
Year:
2013

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Abstract

The Fibonacci (p, 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. Klavzar, On median nature and enumerative properties of Fibonacci-like cubes, Discrete Math. 299 (2005) 145-153]. The question for determining which Fibonacci (p, r)-cubes are median graphs is solved completely in this paper. We show that Fibonacci (p, r)-cubes are median graphs if and only if either r@?p and r@?2, or p=1 and r=n.