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 <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 codeint 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 graphimport 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 graphusing 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 Codepublic static void Main () { int vertices = 3; Console.WriteLine("No. of colors required is: " + Color(vertices));} } // This code is contributed by anuj_67 |
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?> |
Javascript
<script>// Javascript program to find number of colors// required to color a cycle graph// Function that calculates Color// require to color a graph.function Color(vertices){ var 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 codevar vertices = 3;document.write("No. of colors require is: " + Color(vertices)); // This code is contributed by itsok</script> |
Output
No. of colors require is: 3
Complexity Analysis:
- Time Complexity: O(1)
- Space Complexity: O(1)
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