Fibonacci Cube Graph - GeeksforGeeks

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<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 
?> 

Output :

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

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

C++

Java

Python3

C#

PHP

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