Generalized Fibonacci cube Qd（f）, introduced by Ilid, 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 subgr...Generalized Fibonacci cube Qd（f）, introduced by Ilid, 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 Q4 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.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.11671347,11605083)Shandong Provincial Natural Science Foundation(Grant No.ZR2015PA006)Research Fund for the Doctoral Program of Ludong University(Grant No.LY2015006)
文摘Generalized Fibonacci cube Qd（f）, introduced by Ilid, 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 Q4 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.
