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 

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Color required = 2  

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Example 2: Odd Cycle: Number of vertices = 5  

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Color required = 3  

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Implementation:

No. of colors require is: 3

Complexity Analysis:

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