All good (bad) words consisting of 5 blocks

Generalized Fibonacci cube Q d ( f ), introduced by Ilić, Klavžar and Rho, is the graph obtained from the hypercube Q d by removing all vertices that contain f as factor. A word f is good if Q d ( f ) is an isometric subgraph of Q d for all d ≥ 1, and bad otherwise. A non-extendable sequence of cont...

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Bibliographic Details
Published in:Acta mathematica Sinica. English series 2017-06, Vol.33 (6), p.851-860
Main Author: Wei, Jian Xin
Format: Article
Language:English
Subjects:
Digits
Fibonacci numbers
Graph theory
Mathematical analysis
Mathematics
Mathematics and Statistics
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Summary:Generalized Fibonacci cube Q d ( f ), introduced by Ilić, Klavžar and Rho, is the graph obtained from the hypercube Q d by removing all vertices that contain f as factor. A word f is good if Q d ( f ) is an isometric subgraph of Q d for all d ≥ 1, and bad otherwise. A non-extendable sequence of contiguous equal digits in a word μ is called a block of μ . Ilić, Klavžar and Rho shown that all the words consisting of one block are good, and all the words consisting of three blocks are bad. So a natural problem is to study the words consisting of other odd number of blocks. In the present paper, a necessary condition for a word consisting of odd number of blocks being good is given, and all the good (bad) words consisting of 5 blocks is determined.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-017-6134-2