Degree of a Cycle Graph

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 vertx 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 implementaion of the above problem:

Program 1: For 4 vertices cycle graph

C++

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// 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;
}

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Java

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// 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..

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Python3

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# 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

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C#

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//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..

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PHP

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<?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
?>

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Output:

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

Program 2: For 6 vertices cycle graph

C++

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// 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;
}

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Python3

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# 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

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Output:

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


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