# Fibonacci Cube Graph

You are given input as order of graph n (highest number of edges connected to a node), you have to find the number of vertices in a Fibonacci cube graph of order n.**Examples :**

Input : n = 3 Output : 5 Explanation : Fib(n + 2) = Fib(5) = 5 Input : n = 2 Output : 3

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,

Fibonacii series : 1, 1, 2, 3, 5, 8, 13, 21, 34……………….

For input n as order of graph, find the corresponding fibonacci number at the position n + 2.

where F(n) = F(n – 1) + F(n – 2)**Approach : **Find the (n + 2)-th fibonacci number.

Below is the implementation of above approach :

## C++

`// CPP code to find vertices in a fibonacci` `// cube graph of order n` `#include<iostream>` `using` `namespace` `std;` `// function to find fibonacci number` `int` `fib(` `int` `n)` `{` ` ` `if` `(n <= 1)` ` ` `return` `n;` ` ` `return` `fib(n - 1) + fib(n - 2);` `}` `// function for finding number of vertices` `// in fibonacci cube graph` `int` `findVertices (` `int` `n)` `{` ` ` `// return fibonacci number for f(n + 2)` ` ` `return` `fib(n + 2);` `}` `// driver program` `int` `main()` `{` ` ` `// n is the order of the graph` ` ` `int` `n = 3;` ` ` `cout << findVertices(n);` ` ` `return` `0;` `}` |

## Java

`// java code to find vertices in a fibonacci` `// cube graph of order n` `public` `class` `GFG {` ` ` ` ` `// function to find fibonacci number` ` ` `static` `int` `fib(` `int` `n)` ` ` `{` ` ` `if` `(n <= ` `1` `)` ` ` `return` `n;` ` ` `return` `fib(n - ` `1` `) + fib(n - ` `2` `);` ` ` `}` ` ` ` ` `// function for finding number of vertices` ` ` `// in fibonacci cube graph` ` ` `static` `int` `findVertices (` `int` `n)` ` ` `{` ` ` `// return fibonacci number for f(n + 2)` ` ` `return` `fib(n + ` `2` `);` ` ` `}` ` ` ` ` `public` `static` `void` `main(String args[]) {` ` ` ` ` `// n is the order of the graph` ` ` `int` `n = ` `3` `;` ` ` `System.out.println(findVertices(n));` ` ` `}` `}` `// This code is contributed by Sam007` |

## Python3

`# Python3 code to find vertices in` `# a fibonacci cube graph of order n` `# Function to find fibonacci number` `def` `fib(n):` ` ` `if` `n <` `=` `1` `:` ` ` `return` `n` ` ` ` ` `return` `fib(n ` `-` `1` `) ` `+` `fib(n ` `-` `2` `)` `# Function for finding number of` `# vertices in fibonacci cube graph` `def` `findVertices(n):` ` ` `# return fibonacci number` ` ` `# for f(n + 2)` ` ` `return` `fib(n ` `+` `2` `)` `# Driver Code` `if` `__name__ ` `=` `=` `"__main__"` `:` ` ` `# n is the order of the graph` ` ` `n ` `=` `3` ` ` `print` `(findVertices(n))` `# This code is contributed` `# by Rituraj Jain` |

## C#

`// C# code to find vertices in a fibonacci` `// cube graph of order n` `using` `System;` `class` `GFG {` ` ` ` ` `// function to find fibonacci number` ` ` `static` `int` `fib(` `int` `n)` ` ` `{` ` ` `if` `(n <= 1)` ` ` `return` `n;` ` ` `return` `fib(n - 1) + fib(n - 2);` ` ` `}` ` ` ` ` `// function for finding number of` ` ` `// vertices in fibonacci cube graph` ` ` `static` `int` `findVertices (` `int` `n)` ` ` `{` ` ` ` ` `// return fibonacci number for` ` ` `// f(n + 2)` ` ` `return` `fib(n + 2);` ` ` `}` ` ` ` ` `// Driver code` ` ` `static` `void` `Main()` ` ` `{` ` ` ` ` `// n is the order of the graph` ` ` `int` `n = 3;` ` ` ` ` `Console.Write(findVertices(n));` ` ` `}` `}` `// This code is contributed by Sam007` |

## PHP

`<?php` `// PHP code to find vertices in a` `// fibonacci cube graph of order n` `// function to find fibonacci number` `function` `fib(` `$n` `)` `{` ` ` `if` `(` `$n` `<= 1)` ` ` `return` `$n` `;` ` ` `return` `fib(` `$n` `- 1) + fib(` `$n` `- 2);` `}` `// function for finding number of ` `// vertices in fibonacci cube graph` `function` `findVertices (` `$n` `)` `{` ` ` `// return fibonacci number` ` ` `// for f(n + 2)` ` ` `return` `fib(` `$n` `+ 2);` `}` `// Driver Code` `// n is the order of the graph` `$n` `= 3;` `echo` `findVertices(` `$n` `); ` `// This code is contributed by Sam007` `?>` |

## Javascript

`<script>` `// Javascript code to find vertices in a fibonacci` `// cube graph of order n` `// function to find fibonacci number` `function` `fib(n)` `{` ` ` `if` `(n <= 1)` ` ` `return` `n;` ` ` `return` `fib(n - 1) + fib(n - 2);` `}` `// function for finding number of vertices` `// in fibonacci cube graph` `function` `findVertices (n)` `{` ` ` `// return fibonacci number for f(n + 2)` ` ` `return` `fib(n + 2);` `}` `// driver program` `// n is the order of the graph` `var` `n = 3;` `document.write( findVertices(n));` `</script>` |

**Output :**

5

Note that the above code can be optimized to work in O(Log n) using efficient implementations discussed in Program for Fibonacci numbers

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