Acta Mathematica Sinica, English Series

, Volume 33, Issue 6, pp 851–860

# All good (bad) words consisting of 5 blocks

Article

## Abstract

Generalized Fibonacci cube Qd(f), introduced by Ilić, Klavžar and Rho, is the graph obtained from the hypercube Qd by removing all vertices that contain f as factor. A word f is good if Qd(f) is an isometric subgraph of Qd 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.

### Keywords

Generalized Fibonacci cube isometric subgraph good word bad word

05C12 05C60

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