All Good (Bad) Words Consisting of 5 Blocks

作者：Wei, Jian Xin^*

来源：Acta Mathematica Sinica-English Series, 2017, 33(6): 851-860.

DOI：10.1007/s10114-017-6134-2

• Generalized Fibonacci cube
• isometric subgraph
• good word
• bad word

Generalized Fibonacci cube Q(d) (f), introduced by IliAc, Klavzar 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 mu is called a block of mu. Ilic, Klavzar 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.

• 出版日期2017-6
• 单位鲁东大学