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
```

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 ` `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

 ` `

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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Improved By : Sam007, rituraj_jain

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