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++

filter_none

edit
close

play_arrow

link
brightness_4
code

// 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;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// 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

chevron_right


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 [tabby title="C#"]

filter_none

edit
close

play_arrow

link
brightness_4
code

// 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

chevron_right


PHP

filter_none

edit
close

play_arrow

link
brightness_4
code

<?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
?>

chevron_right


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



My Personal Notes arrow_drop_up

Discovering ways to develop a plane for soaring career goals

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.



Improved By : Sam007, rituraj_jain



Article Tags :
Practice Tags :


Be the First to upvote.


Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.