Total number of Spanning trees in a Cycle Graph

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Given the number of vertices in a Cycle graph. The task is to find the Total number of Spanning trees possible.

Note: A cycle/circular graph is a graph that contains only one cycle. A spanning tree is the shortest/minimum path in a graph that covers all the vertices of a graph.

Examples:

Input: Vertices = 3
Output: Total Spanning tree = 3

Input: Vertices = 4
Output: Total Spanning tree = 4

Example 1:

For Cycle Graph with vertices = 3

Spanning Tree possible is 3

Example 2:
For Cycle Graph with vertices = 4

Spanning Tree possible is 4

So, the number of spanning trees will always be equal to the number of vertices in a cycle graph.

Implementation:

C++

// C++ program to find number of
// spanning trees
#include <bits/stdc++.h>
using namespace std;
 
// function that calculates the
// total Spanning tree
int Spanning(int vertices)
{
    int result = 0;
 
    result = vertices;
    return result;
}
 
// Driver code
int main()
{
    int vertices = 4;
 
    cout << "Spanning tree = " << Spanning(vertices);
    return 0;
}

Java

// Java program to find number of 
// spanning trees 
 
import java.io.*;
 
class GFG {
 
// function that calculates the 
// total Spanning tree 
static int Spanning(int vertices) 
{ 
    int result = 0; 
 
    result = vertices; 
    return result; 
} 
 
// Driver code 
    public static void main (String[] args) {
    int vertices = 4; 
 
    System.out.println("Spanning tree = " + Spanning(vertices));
    }
}
// This code is contributed  
// by chandan_jnu..

Python3

# Python program to find number of 
# spanning trees 
 
# function that calculates the 
# total Spanning tree 
def Spanning( vertices):
        result = 0
 
    result = vertices 
    return result 
 
# Driver code 
vertices = 4
print("Spanning tree = ", 
       Spanning(vertices))
 
# This code is contributed
# by Sanjit_Prasad

C#

// C# program to find number 
// of spanning trees
using System;
 
// function that calculates 
// the total Spanning tree
class GFG
{
public int Spanning(int vertices)
{
    int result = 0;
 
    result = vertices;
    return result;
}
 
// Driver code
public static void Main()
{
    GFG g = new GFG();
    int vertices = 4;
 
    Console.WriteLine("Spanning tree = {0}",   
                      g.Spanning(vertices));
}
}
 
// This code is contributed
// by Soumik

PHP

<?php
// PHP program to find number of
// spanning trees
 
// function that calculates the
// total Spanning tree
function Spanning($vertices)
{
    $result = 0;
 
    $result = $vertices;
    return $result;
}
 
// Driver code
$vertices = 4;
 
echo "Spanning tree = " . 
     Spanning($vertices);
      
// This code is contributed 
// by Ankita Saini
?>

Javascript

<script>
 
// Javascript program to find number of
// spanning trees
 
// Function that calculates the
// total Spanning tree
function Spanning(vertices)
{
    result = 0;
    result = vertices;
    return result;
}
 
// Driver code
var vertices = 4;
document.write("Spanning tree = " + 
               Spanning(vertices));
 
// This code is contributed by noob2000
 
</script>

Output

Spanning tree = 4

Time Complexity: O(1)
Auxiliary Space: O(1)

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