Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4650032 | Discrete Mathematics | 2009 | 10 Pages |
Abstract
The Fibonacci cube În is a subgraph of n-dimensional hypercube induced by the vertices without two consecutive ones. Klavžar and Žigert [Fibonacci cubes are the resonance graphs of fibonaccenes, Fibonacci Quart. 43 (2005) 269-276] proved that Fibonacci cubes are precisely the Z-transformation graphs (or resonance graphs) of zigzag hexagonal chains. In this paper, we characterize plane bipartite graphs whose Z-transformation graphs are exactly Fibonacci cubes. If we delete from În(nâ¥3) all the vertices with 1 both in the first and in the last position, we obtain the Lucas cube Ln. We show, however, that none of the Lucas cubes are Z-transformation graphs, and characterize plane bipartite graphs whose Z-transformation graphs are L2kâ² for kâ¥2, which is obtained from L2k by adding two vertices and joining one to 1010â¦10 and the other to 0101â¦01.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Heping Zhang, Lifeng Ou, Haiyuan Yao,