Total number of Spanning trees in a Cycle Graph
Last Updated :
23 Dec, 2022
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 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..
# 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# 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 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
?>
<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>
Time Complexity: O(1)
Auxiliary Space: O(1)