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. Fibonacci cubes were first explicitly defined in Hsu (1993) 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.
In the mathematical field of graph theory, the Fibonaccicubes or Fibonacci networks are a family of undirected graphs with rich recursive properties derived...
technique and the Fibonacci heap data structure, and graphs called Fibonaccicubes used for interconnecting parallel and distributed systems. They also...
demonstrates knowledge of Fibonacci numbers. In L: Change the World (2008), Near is seen arranging sugar cubes in a Fibonacci sequence. In 21 (2008), the...
calculations of pentagons and decagons; his writings influenced that of Fibonacci (Leonardo of Pisa) (c. 1170–1250), who used the ratio in related geometry...
then the subset of vertices indexed by the fibbinary numbers forms a Fibonaccicube as its induced subgraph. Every number has a fibbinary multiple. For...
cube. Divide every face of the cube into nine squares, like a Rubik's Cube. This sub-divides the cube into 27 smaller cubes. Remove the smaller cube in...
Lucas pseudoprimes and Fibonacci pseudoprimes are composite integers that pass certain tests which all primes and very few composite numbers pass: in...
sixth Fibonacci number and the first even, non-prime Fibonacci number. It is also the only positive Fibonacci number aside from 1 that is a perfect cube. 8...
cubes. The trees and hypercube graphs are examples of median graphs. Since the median graphs include the squaregraphs, simplex graphs, and Fibonacci cubes...
theory with more consolidated theories. Integer sequence Fibonacci sequence Golden mean base Fibonacci coding Lucas sequence Padovan sequence Figurate numbers...
closely related Fibonacci sequence. Individual numbers in the Lucas sequence are known as Lucas numbers. Lucas numbers and Fibonacci numbers form complementary...
of cubic equations. In his book Flos, Leonardo de Pisa, also known as Fibonacci (1170–1250), was able to closely approximate the positive solution to...
{\sqrt {5}}} then naturally figures in the closed form expression for the Fibonacci numbers, a formula which is usually written in terms of the golden ratio:...
calculated by means of a recurrence relation similar to that for the Fibonacci numbers, and both sequences of numbers grow exponentially, proportionally...
tiling of the whole plane. Cubing the cube is the analogue in three dimensions of squaring the square: that is, given a cube C, the problem of dividing...
structure of the matchings in these graphs may be visualized using a Fibonaccicube. The largest possible value of the Hosoya index, on a graph with n {\displaystyle...
graph. The simplex graph of the complement graph of a path graph is a Fibonaccicube. The complete subgraphs of G can be given the structure of a median...
Fermat primes, which include 5, 17, 257, and 65537. It is the second Fibonacci prime (and the second Lucas prime), the second Sophie Germain prime, the...
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