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 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