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# Degree of a Cycle Graph

• Difficulty Level : Basic
• Last Updated : 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++

 `// 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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