# 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 : vertices = 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

Implementation:

## 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

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## Javascript

 ``

Output
`No. of colors require is: 3`

Complexity Analysis:

• Time Complexity: O(1)
• Space Complexity: O(1)

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