# Degree of a Cycle Graph

• Difficulty Level : Basic
• Last Updated : 02 Sep, 2022

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 ` `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

 ``

## Javascript

 ``

Output

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

Program 2: For 6 vertices cycle graph

## C++

 `// C++ implementation of above program.`   `#include ` `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

 ``

## Javascript

 ``

Output

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

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