**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 <bits/stdc++.h> ` `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; ` `} ` |

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## 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 ` |

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## 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 ` |

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## 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 ` |

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## PHP

`<?php ` `// PHP program to find number of colors ` `// required to color a cycle graph ` ` ` `// Function that calculates Color ` `// require to color a graph. ` `function` `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 ` `$vertices` `= 3; ` `echo` `"No. of colors required is: "` `, ` ` ` `Color(` `$vertices` `); ` ` ` `// This code is contributed ` `// by anuj_67 ` `?> ` |

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**Output:**

No. of colors require is: 3

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