In the mathematical field of graph theory, 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.

The Fibonacci cube graph of order is a graph on vertices, where is a Fibonacci number, labeled by the Zeckendorf representations of the numbers 0 to and with two vertices connected by an edge iff their labels differ by a single bit (i.e., if the Hamming distance between them is exactly 1).

2022年10月3日 · A Fibonacci Cube Graph is similar to hypercube graph, but with a fibonacci number of vertices. In fibonacci cube graph only 1 vertex has degree n rest all has degree less than n. Fibonacci cube graph of order n has F(n + 2) vertices, where F(n) is a n-th fibonacci number, Fibonacci series : 1, 1, 2, 3, 5, 8, 13, 21, 34……………….

Fibonacci Cubes have been an extremely popular area of research since the 1990s. This unique compendium features the state of research into Fibonacci Cubes. It expands the knowledge in graph theoretic and combinatorial properties of Fibonacci Cubes and their variants.

In mathematics, the Fibonacci sequence is a sequence in which each element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted F n .

In this paper a survey on Fibonacci cubes is given with an emphasis on their structure, including representations, recursive construction, hamiltonicity, degree sequence and other enumeration results. Their median nature that leads to a fast recognition algorithm is discussed.

2011年11月23日 · In this paper a survey on Fibonacci cubes is given with an emphasis on their structure, including representations, recursive construction, hamiltonicity, degree sequence and other enumeration results. Their median nature that …

They are the cubes of the counting numbers (they start at 1): etc... 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... The Fibonacci Sequence is found by adding the two numbers before it together. Can you figure out the next few numbers?

2003年7月31日 · A Fibonacci string of order \(n\) is a binary string of length \(n\) with no two consecutive ones. The Fibonacci cube \(\Gamma_n\) is the subgraph of the hypercube \(Q_n\) induced by the set of Fibonacci strings of order \(n\). For positive integers \(i, n\), with \(n \geq i\), the \(i\)th extended Fibonacci cube is the vertex-induced subgraph ...

2024年12月31日 · The Fibonacci cube \(\Gamma_{n}\) can be obtained from \(Q_{n}\) by removing all vertices that contain two consecutive \(1\) s. It is a graph family that have been studied as alternatives for the classical hypercube topology for interconnection networks.