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