Fibonacci (p,r)-cubes as Cartesian products

The Fibonacci (p,r)-cube Γn(p,r) is the subgraph of Qn induced on binary words of length n in which there are at most r consecutive ones and there are at least p zeros between two substrings of ones. These cubes simultaneously generalize several interconnection networks, notably hypercubes, Fibonacc...

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Bibliographic Details
Published inDiscrete mathematics Vol. 328; pp. 23 - 26
Main Authors Klavžar, Sandi, Rho, Yoomi
Format Journal Article
LanguageEnglish
Published Elsevier B.V 06.08.2014
Subjects
Cartesian
Cartesian product
Cubes
Fibonacci [formula omitted]-cube
Hypercube
Hypercubes
Interconnection
Mathematical analysis
Networks
Cartesian product
Hypercube
Fibonacci (p,r)-cube
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Summary:The Fibonacci (p,r)-cube Γn(p,r) is the subgraph of Qn induced on binary words of length n in which there are at most r consecutive ones and there are at least p zeros between two substrings of ones. These cubes simultaneously generalize several interconnection networks, notably hypercubes, Fibonacci cubes, and postal networks. In this note it is proved that Γn(p,r) is a non-trivial Cartesian product if and only if p=1 and r=n≥2, or p=r=2 and n≥2, or n=p=3 and r=2. This rounds a result from Ou et al. (2011) asserting that Γn(2,2) are non-trivial Cartesian products.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2014.03.027