# Coloring a Cycle Graph

Cycle:- cycle is a path of edges and vertices wherein a vertex is reachable from itself. or in other words, it is a Closed walk.
Even Cycle:- In which Even number of vertices is present is known as Even Cycle.
Odd Cycle:- In which Odd number of Vertices is present is known as Odd Cycle.

Given the number of vertices in a Cyclic Graph. The task is to determine the Number of colors required to color the graph so that No two Adjacent vertices have the same color.

Approach:

If the no. of vertices is Even then it is Even Cycle and to color such graph we require 2 colors.
If the no. of vertices is Odd then it is Odd Cycle and to color such graph we require 3 colors.

Examples:

```Input : vertices = 3
Output : No. of colors require is: 3

Input : verices = 4
Output : No. of colors require is: 2
```

Example 1: Even Cycle: Number of vertices = 4 Color required = 2 Example 2: Odd Cycle: Number of vertices = 5 Color required = 3 ## C++

 `// CPP program to find number of colors ` `// required to color a cycle graph ` `#include ` `using` `namespace` `std; ` ` `  `// Function that calculates Color ` `// require to color a graph. ` `int` `Color(``int` `vertices) ` `{ ` `    ``int` `result = 0; ` ` `  `    ``// Check if number of vertices ` `    ``// is odd or even. ` `    ``// If number of vertices is even ` `    ``// then color require is 2 otherwise 3 ` `    ``if` `(vertices % 2 == 0) ` `        ``result = 2; ` `    ``else` `        ``result = 3; ` ` `  `    ``return` `result; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `vertices = 3; ` `    ``cout << ``"No. of colors require is: "` `<< Color(vertices); ` `    ``return` `0; ` `} `

## Java

 `// Java program to find number of colors ` `// required to color a cycle graph ` `import` `java.io.*;  ` ` `  `class` `GFG {  ` `   `  `    ``// Function that calculates Color  ` `    ``// require to color a graph.   ` `    ``static` `int` `Color(``int` `vertices)  ` `    ``{  ` `        ``int` `result = ``0``;  ` `   `  `        ``// Check if number of vertices  ` `        ``// is odd or even.  ` `        ``// If number of vertices is even  ` `        ``// then color require is 2 otherwise 3  ` `        ``if` `(vertices % ``2` `== ``0``)  ` `            ``result = ``2``;  ` `        ``else` `            ``result = ``3``;  ` `       `  `        ``return` `result;  ` `    ``}   ` `       `  `    ``// Driver program to test above function  ` `    ``public` `static` `void` `main (String[] args)  ` `    ``{  ` `        ``int` `vertices = ``3``;  ` `         `  `        ``System.out.println(``"No. of colors require is: "` `+ Color(vertices)); ` `           `  `    ``}  ` `}  ` ` `  `// this code is contributed by Naman_Garg `

## Python3

 `# Naive Python3 Program to  ` `# find the number of colors ` `# required to color a cycle graph   ` `   `  `# Function to find Color required. ` `def` `Color(vertices):   ` `   `  `    ``result ``=` `0`  `   `  `    ``# Check if number of vertices  ` `    ``# is odd or even.  ` `    ``# If number of vertices is even  ` `    ``# then color require is 2 otherwise 3  ` `    ``if` `(vertices ``%` `2` `=``=` `0``): ` `        ``result ``=` `2` `    ``else``: ` `        ``result ``=` `3`  `   `  `    ``return` `result ` `   `  `# Driver Code  ` `if` `__name__``=``=``'__main__'``: ` `    ``vertices ``=` `3` `    ``print` `(``"No. of colors require is:"``,Color(vertices)) ` ` `  `# this code is contributed by Naman_Garg `

## C#

 `// C# program to find number of colors ` `// required to color a cycle graph ` `using` `System;  ` ` `  `class` `GFG ` `{  ` ` `  `// Function that calculates Color  ` `// require to color a graph.  ` `static` `int` `Color(``int` `vertices)  ` `{  ` `    ``int` `result = 0;  ` ` `  `    ``// Check if number of vertices  ` `    ``// is odd or even.  ` `    ``// If number of vertices is even  ` `    ``// then color require is 2 otherwise 3  ` `    ``if` `(vertices % 2 == 0)  ` `        ``result = 2;  ` `    ``else` `        ``result = 3;  ` ` `  `    ``return` `result;  ` `}  ` ` `  `// Driver Code ` `public` `static` `void` `Main ()  ` `{  ` `    ``int` `vertices = 3;  ` `     `  `    ``Console.WriteLine(``"No. of colors required is: "` `+  ` `                                   ``Color(vertices)); ` `}  ` `}  ` ` `  `// This code is contributed by anuj_67 `

## PHP

 ` `

Output:

```No. of colors require is: 3
```

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