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