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:
// 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;
} |
// 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 |
# 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# 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 // 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 ?> |
<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 code var vertices = 3;
document.write( "No. of colors require is: " +
Color(vertices));
// This code is contributed by itsok </script> |
No. of colors require is: 3
Complexity Analysis:
- Time Complexity: O(1)
- Space Complexity: O(1)