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

The Fibonacci ( p , r )-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...

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Bibliographic Details
Published in:Discrete mathematics 2011-08, Vol.311 (16), p.1681-1692
Main Authors: Ou, Lifeng, Zhang, Heping, Yao, Haiyuan
Format: Article
Language:English
Subjects:
[formula omitted]-transformation graph
Algebra
Applied sciences
Combinatorics
Combinatorics. Ordered structures
Computer science
control theory
systems
Cubes
Exact sciences and technology
Fibonacci [formula omitted]-cube
Graph theory
Graphs
Information retrieval. Graph
Interconnection
Joints
Mathematical analysis
Mathematics
Networks
Partial differential equations
Perfect matching
Planes
Resonance graph
Sciences and techniques of general use
Theoretical computing
Topology
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Summary:The Fibonacci ( p , r )-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 Z -transformation graphs (also called resonance graphs) of fibonaccenes, i.e. zigzag hexagonal chains. In this paper, we determine all Fibonacci ( p , r )-cubes which can be the Z -transformation graphs of perfect matchings of plane (bipartite) graphs.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2011.04.002