All Good(Bad) Words Consisting of 5 Blocks

Generalized Fibonacci cube Qd（f）, introduced by Ilic, Klavzar 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. 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.