摘要
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.
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.
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)