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++
#include <bits/stdc++.h>
using namespace std;
int getnumberOfEdges( int numberOfVertices)
{
int numberOfEdges = 0;
numberOfEdges = numberOfVertices;
return numberOfEdges;
}
int getDegree( int numberOfVertices)
{
int degree;
degree = 2 * numberOfVertices;
return degree;
}
int main()
{
int numberOfVertices = 4;
cout << "For numberOfVertices = "
<< numberOfVertices
<< "\nDegree = "
<< getDegree(numberOfVertices)
<< "\nNumber of Edges = "
<< getnumberOfEdges(numberOfVertices);
return 0;
}
|
Java
import java.io.*;
class GFG {
static int getnumberOfEdges( int numberOfVertices)
{
int numberOfEdges = 0 ;
numberOfEdges = numberOfVertices;
return numberOfEdges;
}
static int getDegree( int numberOfVertices)
{
int degree;
degree = 2 * numberOfVertices;
return degree;
}
public static void main(String[] args)
{
int numberOfVertices = 4 ;
System.out.print( "For numberOfVertices = "
+ numberOfVertices
+ "\nDegree = "
+ getDegree(numberOfVertices)
+ "\nNumber of Edges = "
+ getnumberOfEdges(numberOfVertices));
}
}
|
Python3
def getnumberOfEdges(numberOfVertices) :
numberOfEdges = numberOfVertices
return numberOfEdges
def getDegree(numberOfVertices) :
degree = 2 * numberOfVertices
return degree
if __name__ = = "__main__" :
numberOfVertices = 4
print ( "For numberOfVertices =" , numberOfVertices,
"\nDegree =" , getDegree(numberOfVertices),
"\nNumber of Edges =" , getnumberOfEdges(numberOfVertices))
|
C#
using System;
class GFG {
static int getnumberOfEdges( int numberOfVertices)
{
int numberOfEdges = 0;
numberOfEdges = numberOfVertices;
return numberOfEdges;
}
static int getDegree( int numberOfVertices)
{
int degree;
degree = 2 * numberOfVertices;
return degree;
}
public static void Main()
{
int numberOfVertices = 4;
Console.WriteLine( "For numberOfVertices = "
+ numberOfVertices
+ "\nDegree = "
+ getDegree(numberOfVertices)
+ "\nNumber of Edges = "
+ getnumberOfEdges(numberOfVertices));
}
}
|
PHP
<?php
function getnumberOfEdges( $numberOfVertices )
{
$numberOfEdges = 0;
$numberOfEdges = $numberOfVertices ;
return $numberOfEdges ;
}
function getDegree( $numberOfVertices )
{
$degree = 2 * $numberOfVertices ;
return $degree ;
}
$numberOfVertices = 4;
echo ( "For numberOfVertices = " );
echo ( $numberOfVertices );
echo ( "\nDegree = " );
echo getDegree( $numberOfVertices );
echo ( "\nNumber of Edges = " );
echo getnumberOfEdges( $numberOfVertices );
?>
|
Javascript
<script>
function getnumberOfEdges(numberOfVertices)
{
var numberOfEdges = 0;
numberOfEdges = numberOfVertices;
return numberOfEdges;
}
function getDegree(numberOfVertices)
{
var degree;
degree = 2 * numberOfVertices;
return degree;
}
var numberOfVertices = 4;
document.write( "For numberOfVertices = " +
numberOfVertices + "<br>Degree = " +
getDegree(numberOfVertices) +
"<br>Number of Edges = " +
getnumberOfEdges(numberOfVertices));
</script>
|
Output
For numberOfVertices = 4
Degree = 8
Number of Edges = 4
Program 2: For 6 vertices cycle graph
C++
#include <bits/stdc++.h>
using namespace std;
int getnumberOfEdges( int numberOfVertices)
{
int numberOfEdges = 0;
numberOfEdges = numberOfVertices;
return numberOfEdges;
}
int getDegree( int numberOfVertices)
{
int degree;
degree = 2 * numberOfVertices;
return degree;
}
int main()
{
int numberOfVertices = 6;
cout << "For numberOfVertices = "
<< numberOfVertices
<< "\nDegree = "
<< getDegree(numberOfVertices)
<< "\nNumber of Edges = "
<< getnumberOfEdges(numberOfVertices);
return 0;
}
|
Java
class GfG {
static int getnumberOfEdges( int numberOfVertices)
{
int numberOfEdges = 0 ;
numberOfEdges = numberOfVertices;
return numberOfEdges;
}
static int getDegree( int numberOfVertices)
{
int degree;
degree = 2 * numberOfVertices;
return degree;
}
public static void main(String[] args)
{
int numberOfVertices = 6 ;
System.out.println( "For numberOfVertices = "
+ numberOfVertices + "\nDegree = "
+ getDegree(numberOfVertices)
+ "\nNumber of Edges = "
+ getnumberOfEdges(numberOfVertices));
}
}
|
Python3
def getnumberOfEdges(numberOfVertices):
numberOfEdges = 0
numberOfEdges = numberOfVertices
return numberOfEdges
def getDegree(numberOfVertices):
degree = 2 * numberOfVertices
return degree
if __name__ = = "__main__" :
numberOfVertices = 6
print ( "For numberOfVertices = " ,
numberOfVertices, "\nDegree = " ,
getDegree(numberOfVertices),
"\nNumber of Edges = " ,
getnumberOfEdges(numberOfVertices))
|
C#
class GfG {
static int getnumberOfEdges( int numberOfVertices)
{
int numberOfEdges = 0;
numberOfEdges = numberOfVertices;
return numberOfEdges;
}
static int getDegree( int numberOfVertices)
{
int degree;
degree = 2 * numberOfVertices;
return degree;
}
static void Main()
{
int numberOfVertices = 6;
System.Console.WriteLine( "For numberOfVertices = "
+ numberOfVertices + "\nDegree = "
+ getDegree(numberOfVertices)
+ "\nNumber of Edges = "
+ getnumberOfEdges(numberOfVertices));
}
}
|
PHP
<?php
function getnumberOfEdges( $numberOfVertices )
{
$numberOfEdges = 0;
$numberOfEdges = $numberOfVertices ;
return $numberOfEdges ;
}
function getDegree( $numberOfVertices )
{
$degree = 0;
$degree = 2 * $numberOfVertices ;
return $degree ;
}
$numberOfVertices = 6;
echo "For numberOfVertices = " . $numberOfVertices .
"\nDegree = " . getDegree( $numberOfVertices ) .
"\nNumber of Edges = " .
getnumberOfEdges( $numberOfVertices );
?>
|
Javascript
<script>
function getnumberOfEdges(numberOfVertices)
{
let numberOfEdges = 0;
numberOfEdges = numberOfVertices;
return numberOfEdges;
}
function getDegree(numberOfVertices)
{
let degree;
degree = 2 * numberOfVertices;
return degree;
}
let numberOfVertices = 6;
document.write( "For numberOfVertices = "
+ numberOfVertices + "<br>Degree = "
+ getDegree(numberOfVertices)
+ "<br>Number of Edges = "
+ getnumberOfEdges(numberOfVertices));
</script>
|
Output
For numberOfVertices = 6
Degree = 12
Number of Edges = 6
Last Updated :
02 Sep, 2022
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