Degree of a Cycle Graph - GeeksforGeeks

16 Jun, 2021
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++
Java
Python3
C#
PHP
Javascript
// 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 degreeint 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 codeint 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 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 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 degreedef 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# 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 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 $numberOfEdges;} // function that calculates the degreefunction getDegree($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 resultecho ("For numberOfVertices = ");echo ($numberOfVertices);echo ("\nDegree = ");echo getDegree($numberOfVertices);echo("\nNumber of Edges = ");echo getnumberOfEdges($numberOfVertices); // This code is contributed by Shivi_Aggarwal?>
<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 degreefunction 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 verticesvar numberOfVertices = 4; // Find the numberOfEdges and degree// from the numberOfVertices// and print the resultdocument.write("For numberOfVertices = " +               numberOfVertices + "<br>Degree = " +               getDegree(numberOfVertices) +               "<br>Number of Edges = " +               getnumberOfEdges(numberOfVertices)); // This code is contributed by itsok </script>
For numberOfVertices = 4
Degree = 8
Number of Edges = 4
 
Program 2: For 6 vertices cycle graph  
C++
Java
Python3
C#
PHP
Javascript
// 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 degreeint 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 codeint 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 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
# 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 degreedef getDegree(numberOfVertices):     # The degree of the cycle graph    # will be twice the numberOfVertices    degree = 2 * numberOfVertices     # return the degree    return degree # Driver codeif __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# 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 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 $numberOfEdges;} // function that calculates the degreefunction getDegree($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 resultecho "For numberOfVertices = " . $numberOfVertices .     "\nDegree = " . getDegree($numberOfVertices) .     "\nNumber of Edges = " .      getnumberOfEdges($numberOfVertices); // This code is contributed by mits?>
<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>
For numberOfVertices = 6
Degree = 12
Number of Edges = 6
 
Shivi_Aggarwal
ankthon
ukasp
vt_m
Rajput-Ji
Mithun Kumar
itsok
avanitrachhadiya2155
arorakashish0911
Data Structures-Graph
graph-cycle
C++ Programs
Graph
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