O-Fibonacci (p,r)-cube as Cartesian products

2019/10/14 by Jianxin Wei, Guangfu Wang, Wei, Jianxin +1
Computer Science · Engineering · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Interconnection Networks and Systems #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1910.05891

openalex publication_date 2019/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p ,r and n be positive integers. Then the O-Fibonacci (p,r)-cube OΓ^(p,r)_n is the subgraph of Q_n induced on the binary words in which there is at least p-1 zeros between any two 1s and there is at most r consecutive 10^p-1. These cubes include a wide range of cubes as their special cases, such as hypercubes, Fibonacci cubes, and postal networks. In this note it is proved that OΓ^(p,r)_n is a non-trivial Cartesian product if and only if p=1 and r≥ n≥2.

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