Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5776836 | Discrete Mathematics | 2017 | 7 Pages |
Abstract
The generalized Fibonacci Qd(f) is defined as the graph obtained from the d-cube Qd by removing all vertices that contain a given binary string f as a contiguous substring. This idea was introduced by IliÄ, Klavžar and Rho. A binary string f is called isometric if Qd(f) is an isometric subgraph of Qd for all dâ¥1, otherwise it is called non-isometric. In this paper, we prove that a string f is isometric if and only if fn is isometric for any nâ¥1. This result can help us to construct more isometric strings and significantly increase the number of isometric strings.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Jianxin Wei, Yujun Yang, Guangfu Wang,