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Fibonacci cube
The Fibonacci cubes or Fibonacci networks are a family of undirected graphs with rich recursive properties derived from its origin in number theory. Mathematically they are similar to the hypercube graphs, but with a Fibonacci number of vertices. Fibonacci cubes were first explicitly defined in in the context of interconnection topologies for connecting parallel or distributed systems. They have also been applied in chemical graph theory.
The Fibonacci cube may be defined in terms of Fibonacci codes and Hamming distance, independent sets of vertices in path graphs, or via distributive lattices.
==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 ''F''''n'' + 2 labels possible, where ''F''''n'' denotes the ''n''th Fibonacci number, and therefore there are ''F''''n'' + 2 vertices in the Fibonacci cube of order ''n''.
The nodes of such a network may be assigned consecutive integers from 0 to ''F''''n'' + 2 − 1; the bitstrings corresponding to these numbers are given by their Zeckendorf representations.〔, pp. 3–4.〕
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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