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C++ Program to Find Chromatic Index of Cyclic Graphs



C++ Program to Find Chromatic Index of Cyclic Graphs

- This algorithm finds the chromatic index of the given cyclic graph.
- The chromatic index is the maximum number of color needed for the edge coloring of the given graph.

- This algorithm takes the input of the number of vertexes and the number of edges in the graph.
- It takes the input of vertex pairs for the given number of edges.
- It assigns a color to edges without assigning the same color to two adjacent edges.
- It prints the number of colors used in edge coloring.
- Exit.

 #include<iostream>
 
using namespace std;
 
// A function to color edges of the graph.
int EdgeColoring(int edge[][3], int e)
{
	int i, col, j, max = -1;
	// Loop to assign a valid color to every edge 'i'.
	for(i = 0; i < e; i++)
	{
		col = 1;
		flag:
		// Assign a color and then check its validity.
		edge[i][2] = col;
		for(j = 0; j < e; j++)
		{
			if(j == i)
				continue;
 
			// Check the colors of the edges adjacent to the edge i.
			if(edge[j][0] == edge[i][0] || edge[j][0] == edge[i][1] || edge[j][1] == edge[i][0] || edge[j][1] == edge[i][1])
			{
				// If the color matches then goto line 11 and assign next color to the edge and check again.
				if(edge[j][2] == edge[i][2])
				{
					col++;
					goto flag;
				}
			}
		}
	}
 
	// Find the coloring index and return it, to main.
	for(i = 0; i < e; i++)
	{
		if(max < edge[i][2])
			max = edge[i][2];
	}
	return max;
}
 
int main()
{
	int i, v, e, j, max = -1;
 
	// take the input of the number of vertex and edges.
	cout<<"Enter the number of vertexes of the graph: ";
	cin>>v;
	cout<<"Enter the number of edges of the graph: ";
	cin>>e;
	int edge[e][3];
 
	// Take the input of the adjacent vertex pairs of the given graph.
	for(i = 0; i < e; i++)
	{
		cout<<"\nEnter the vertex pair for edge "<<i+1;
		cout<<"\nV(1): ";
		cin>>edge[i][0];
		cout<<"V(2): ";
		cin>>edge[i][1];
 
		edge[i][2] = -1;
	}
 
	// Print the chromatic index.
	cout<<"\n\nThe chromatic index of the given graph is: "<<EdgeColoring(edge , e);
 
	// Print the edge color for the edges of the given graph.
	for(i = 0; i < e; i++)
		cout<<"\nThe color of the edge between vertex V(1):"<<edge[i][0]<<" and V(2):"<<edge[i][1]<<" is: color"<<edge[i][2]<<".";
 
	return 0;
}