Definition
Like the hypercube graph, the vertices of the Fibonacci cube of order n may be labeled with bitstrings of length n, in such a way that two vertices are adjacent whenever their labels differ in a single bit. However, in a Fibonacci cube, the only labels that are allowed are bitstrings with no two consecutive 1 bits. There are Fn + 2 labels possible, where Fn denotes the nth Fibonacci number, and therefore there are Fn + 2 vertices in the Fibonacci cube of order n.
The nodes of such a network may be assigned consecutive integers from 0 to Fn + 2; the bitstrings corresponding to these numbers are given by their Zeckendorf representations.
Read more about this topic: Fibonacci Cube
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