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Degree of a Cycle Graph

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  • Difficulty Level : Basic
  • Last Updated : 02 Sep, 2022
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Given the number of vertices in a Cycle Graph. The task is to find the Degree and the number of Edges of the cycle graph.

Degree: Degree of any vertex is defined as the number of edge Incident on it.

Cycle Graph: In graph theory, a graph that consists of single cycle is called a cycle graph or circular graph. The cycle graph with n vertices is called Cn

Properties of Cycle Graph:-  

  • It is a Connected Graph.
  • A Cycle Graph or Circular Graph is a graph that consists of a single cycle.
  • In a Cycle Graph number of vertices is equal to number of edges.
  • A Cycle Graph is 2-edge colorable or 2-vertex colorable, if and only if it has an even number of vertices.
  • A Cycle Graph is 3-edge colorable or 3-edge colorable, if and only if it has an odd number of vertices.
  • In a Cycle Graph, Degree of each vertex in a graph is two.
  • The degree of a Cycle graph is 2 times the number of vertices. As each edge is counted twice.

Examples:  

Input: Number of vertices = 4
Output: Degree is 8
        Edges are 4
Explanation: 
The total edges are 4 
and the Degree of the Graph is 8
as 2 edge incident on each of 
the vertices i.e on a, b, c, and d. 

Input: number of vertices = 5
Output: Degree is 10
        Edges are 5

Below is the implementation of the above problem:

Program 1: For 4 vertices cycle graph  

C++




// C++ implementation of above program.
 
#include <bits/stdc++.h>
using namespace std;
 
// function that calculates the
// number of Edge in a cycle graph.
int getnumberOfEdges(int numberOfVertices)
{
    int numberOfEdges = 0;
 
    // The numberOfEdges of the cycle graph
    // will be same as the numberOfVertices
    numberOfEdges = numberOfVertices;
 
    // return the numberOfEdges
    return numberOfEdges;
}
 
// function that calculates the degree
int getDegree(int numberOfVertices)
{
    int degree;
 
    // The degree of the cycle graph
    // will be twice the numberOfVertices
    degree = 2 * numberOfVertices;
 
    // return the degree
    return degree;
}
 
// Driver code
int main()
{
 
    // Get the number of vertices
    int numberOfVertices = 4;
 
    // Find the numberOfEdges and degree
    // from the numberOfVertices
    // and print the result
    cout << "For numberOfVertices = "
         << numberOfVertices
         << "\nDegree = "
         << getDegree(numberOfVertices)
         << "\nNumber of Edges = "
         << getnumberOfEdges(numberOfVertices);
 
    return 0;
}

Java




// Java implementation of above program.
import java.io.*;
 
class GFG {
 
    // function that calculates the
    // number of Edge in a cycle graph.
    static int getnumberOfEdges(int numberOfVertices)
    {
        int numberOfEdges = 0;
 
        // The numberOfEdges of the cycle graph
        // will be same as the numberOfVertices
        numberOfEdges = numberOfVertices;
 
        // return the numberOfEdges
        return numberOfEdges;
    }
 
    // function that calculates the degree
    static int getDegree(int numberOfVertices)
    {
        int degree;
 
        // The degree of the cycle graph
        // will be twice the numberOfVertices
        degree = 2 * numberOfVertices;
 
        // return the degree
        return degree;
    }
 
    // Driver code
    public static void main(String[] args)
    {
        // Get the number of vertices
        int numberOfVertices = 4;
 
        // Find the numberOfEdges and degree
        // from the numberOfVertices
        // and print the result
        System.out.print("For numberOfVertices = "
                         + numberOfVertices
                         + "\nDegree = "
                         + getDegree(numberOfVertices)
                         + "\nNumber of Edges = "
                         + getnumberOfEdges(numberOfVertices));
    }
}
 
// This code is contributed by anuj_67..

Python3




# Python3 implementation of above program.
 
# function that calculates the
# number of Edge in a cycle graph.
def getnumberOfEdges(numberOfVertices) :
 
    # The numberOfEdges of the cycle graph
    # will be same as the numberOfVertices
    numberOfEdges = numberOfVertices
 
    # return the numberOfEdges
    return numberOfEdges
 
# function that calculates the degree
def getDegree(numberOfVertices) :
 
    # The degree of the cycle graph
    # will be twice the numberOfVertices
    degree = 2 * numberOfVertices
 
    # return the degree
    return degree
 
 
# Driver code    
if __name__ == "__main__" :
 
    # Get the number of vertices
    numberOfVertices = 4
 
    # Find the numberOfEdges and degree
    # from the numberOfVertices
    # and print the result
    print("For numberOfVertices =", numberOfVertices,
          "\nDegree =", getDegree(numberOfVertices),
          "\nNumber of Edges =", getnumberOfEdges(numberOfVertices))
 
 
# This code is contributed by ANKITRAI1

C#




// C# implementation of above program.
using System;
 
class GFG {
 
    // function that calculates the
    // number of Edge in a cycle graph.
    static int getnumberOfEdges(int numberOfVertices)
    {
        int numberOfEdges = 0;
 
        // The numberOfEdges of the cycle graph
        // will be same as the numberOfVertices
        numberOfEdges = numberOfVertices;
 
        // return the numberOfEdges
        return numberOfEdges;
    }
 
    // function that calculates the degree
    static int getDegree(int numberOfVertices)
    {
        int degree;
 
        // The degree of the cycle graph
        // will be twice the numberOfVertices
        degree = 2 * numberOfVertices;
 
        // return the degree
        return degree;
    }
 
    // Driver code
    public static void Main()
    {
        // Get the number of vertices
        int numberOfVertices = 4;
 
        // Find the numberOfEdges and degree
        // from the numberOfVertices
        // and print the result
        Console.WriteLine("For numberOfVertices = "
                          + numberOfVertices
                          + "\nDegree = "
                          + getDegree(numberOfVertices)
                          + "\nNumber of Edges = "
                          + getnumberOfEdges(numberOfVertices));
    }
}
 
// This code is contributed by anuj_67..

PHP




<?php
// PHP implementation of above program
 
// function that calculates the
// number of Edge in a cycle graph.
function getnumberOfEdges($numberOfVertices)
{
    $numberOfEdges = 0;
 
    // The numberOfEdges of the cycle graph
    // will be same as the numberOfVertices
    $numberOfEdges = $numberOfVertices;
 
    // return the numberOfEdges
    return $numberOfEdges;
}
 
// function that calculates the degree
function getDegree($numberOfVertices)
{
     
 
    // The degree of the cycle graph
    // will be twice the numberOfVertices
    $degree = 2 * $numberOfVertices;
 
    // return the degree
    return $degree;
}
 
// Driver code
 
// Get the number of vertices
$numberOfVertices = 4;
 
// Find the numberOfEdges and degree
// from the numberOfVertices
// and print the result
echo ("For numberOfVertices = ");
echo ($numberOfVertices);
echo ("\nDegree = ");
echo getDegree($numberOfVertices);
echo("\nNumber of Edges = ");
echo getnumberOfEdges($numberOfVertices);
 
// This code is contributed by Shivi_Aggarwal
?>

Javascript




<script>
 
// Javascript implementation of above program.
 
// function that calculates the
// number of Edge in a cycle graph.
function getnumberOfEdges(numberOfVertices)
{
    var numberOfEdges = 0;
 
    // The numberOfEdges of the cycle graph
    // will be same as the numberOfVertices
    numberOfEdges = numberOfVertices;
 
    // return the numberOfEdges
    return numberOfEdges;
}
 
// function that calculates the degree
function getDegree(numberOfVertices)
{
    var degree;
 
    // The degree of the cycle graph
    // will be twice the numberOfVertices
    degree = 2 * numberOfVertices;
 
    // return the degree
    return degree;
}
 
// Driver code
 
// Get the number of vertices
var numberOfVertices = 4;
 
// Find the numberOfEdges and degree
// from the numberOfVertices
// and print the result
document.write("For numberOfVertices = " +
               numberOfVertices + "<br>Degree = " +
               getDegree(numberOfVertices) +
               "<br>Number of Edges = " +
               getnumberOfEdges(numberOfVertices));
 
// This code is contributed by itsok
 
</script>

Output

For numberOfVertices = 4
Degree = 8
Number of Edges = 4

Program 2: For 6 vertices cycle graph 

C++




// C++ implementation of above program.
 
#include <bits/stdc++.h>
using namespace std;
 
// function that calculates the
// number of Edge in a cycle graph.
int getnumberOfEdges(int numberOfVertices)
{
    int numberOfEdges = 0;
 
    // The numberOfEdges of the cycle graph
    // will be same as the numberOfVertices
    numberOfEdges = numberOfVertices;
 
    // return the numberOfEdges
    return numberOfEdges;
}
 
// function that calculates the degree
int getDegree(int numberOfVertices)
{
    int degree;
 
    // The degree of the cycle graph
    // will be twice the numberOfVertices
    degree = 2 * numberOfVertices;
 
    // return the degree
    return degree;
}
 
// Driver code
int main()
{
 
    // Get the number of vertices
    int numberOfVertices = 6;
 
    // Find the numberOfEdges and degree
    // from the numberOfVertices
    // and print the result
    cout << "For numberOfVertices = "
         << numberOfVertices
         << "\nDegree = "
         << getDegree(numberOfVertices)
         << "\nNumber of Edges = "
         << getnumberOfEdges(numberOfVertices);
 
    return 0;
}

Java




// Java implementation of above program.
class GfG {
 
    // function that calculates the
    // number of Edge in a cycle graph.
    static int getnumberOfEdges(int numberOfVertices)
    {
        int numberOfEdges = 0;
 
        // The numberOfEdges of the cycle graph
        // will be same as the numberOfVertices
        numberOfEdges = numberOfVertices;
 
        // return the numberOfEdges
        return numberOfEdges;
    }
 
    // function that calculates the degree
    static int getDegree(int numberOfVertices)
    {
        int degree;
 
        // The degree of the cycle graph
        // will be twice the numberOfVertices
        degree = 2 * numberOfVertices;
 
        // return the degree
        return degree;
    }
 
    // Driver code
    public static void main(String[] args)
    {
 
        // Get the number of vertices
        int numberOfVertices = 6;
 
        // Find the numberOfEdges and degree
        // from the numberOfVertices
        // and print the result
        System.out.println("For numberOfVertices = "
                           + numberOfVertices + "\nDegree = "
                           + getDegree(numberOfVertices)
                           + "\nNumber of Edges = "
                           + getnumberOfEdges(numberOfVertices));
    }
}
 
// This code contributed by Rajput-Ji

Python3




# Python 3 implementation of above program
 
# function that calculates the
# number of Edge in a cycle graph.
def getnumberOfEdges(numberOfVertices):
 
    numberOfEdges = 0
 
    # The numberOfEdges of the cycle graph
    # will be same as the numberOfVertices
    numberOfEdges = numberOfVertices
 
    # return the numberOfEdges
    return numberOfEdges
 
# function that calculates the degree
def getDegree(numberOfVertices):
 
    # The degree of the cycle graph
    # will be twice the numberOfVertices
    degree = 2 * numberOfVertices
 
    # return the degree
    return degree
 
# Driver code
if __name__ == "__main__":
     
    # Get the number of vertices
    numberOfVertices = 6
 
    # Find the numberOfEdges and degree
    # from the numberOfVertices
    # and print the result
    print("For numberOfVertices = ",
           numberOfVertices, "\nDegree = ",
               getDegree(numberOfVertices),
          "\nNumber of Edges = ",
        getnumberOfEdges(numberOfVertices))
 
# This code is contributed by ChitraNayal

C#




// C# implementation of above program.
class GfG {
 
    // function that calculates the
    // number of Edge in a cycle graph.
    static int getnumberOfEdges(int numberOfVertices)
    {
        int numberOfEdges = 0;
 
        // The numberOfEdges of the cycle graph
        // will be same as the numberOfVertices
        numberOfEdges = numberOfVertices;
 
        // return the numberOfEdges
        return numberOfEdges;
    }
 
    // function that calculates the degree
    static int getDegree(int numberOfVertices)
    {
        int degree;
 
        // The degree of the cycle graph
        // will be twice the numberOfVertices
        degree = 2 * numberOfVertices;
 
        // return the degree
        return degree;
    }
 
    // Driver code
    static void Main()
    {
 
        // Get the number of vertices
        int numberOfVertices = 6;
 
        // Find the numberOfEdges and degree
        // from the numberOfVertices
        // and print the result
        System.Console.WriteLine("For numberOfVertices = "
                                 + numberOfVertices + "\nDegree = "
                                 + getDegree(numberOfVertices)
                                 + "\nNumber of Edges = "
                                 + getnumberOfEdges(numberOfVertices));
    }
}
 
// This code contributed by mits

PHP




<?php
// PHP implementation of above program.
 
// function that calculates the
// number of Edge in a cycle graph.
function getnumberOfEdges($numberOfVertices)
{
    $numberOfEdges = 0;
 
    // The numberOfEdges of the cycle graph
    // will be same as the numberOfVertices
    $numberOfEdges = $numberOfVertices;
 
    // return the numberOfEdges
    return $numberOfEdges;
}
 
// function that calculates the degree
function getDegree($numberOfVertices)
{
    $degree = 0;
 
    // The degree of the cycle graph
    // will be twice the numberOfVertices
    $degree = 2 * $numberOfVertices;
 
    // return the degree
    return $degree;
}
 
// Driver code
 
// Get the number of vertices
$numberOfVertices = 6;
 
// Find the numberOfEdges and degree
// from the numberOfVertices
// and print the result
echo "For numberOfVertices = " . $numberOfVertices .
     "\nDegree = " . getDegree($numberOfVertices) .
     "\nNumber of Edges = " .
      getnumberOfEdges($numberOfVertices);
 
// This code is contributed by mits
?>

Javascript




<script>
// Javascript implementation of above program
     
    // function that calculates the
    // number of Edge in a cycle graph.
    function getnumberOfEdges(numberOfVertices)
    {
        let numberOfEdges = 0;
  
        // The numberOfEdges of the cycle graph
        // will be same as the numberOfVertices
        numberOfEdges = numberOfVertices;
  
        // return the numberOfEdges
        return numberOfEdges;
    }
    // function that calculates the degree
    function getDegree(numberOfVertices)
    {
        let degree;
  
        // The degree of the cycle graph
        // will be twice the numberOfVertices
        degree = 2 * numberOfVertices;
  
        // return the degree
        return degree;
    }
     
    // Driver code
     
    // Get the number of vertices
    let numberOfVertices = 6;
     
    // Find the numberOfEdges and degree
        // from the numberOfVertices
        // and print the result
    document.write("For numberOfVertices = "
                           + numberOfVertices + "<br>Degree = "
                           + getDegree(numberOfVertices)
                           + "<br>Number of Edges = "
                           + getnumberOfEdges(numberOfVertices));
     
 
// This code is contributed by avanitrachhadiya2155
</script>

Output

For numberOfVertices = 6
Degree = 12
Number of Edges = 6

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