C++ Programming Code Examples
C++ > Computer Graphics Code Examples
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;
}
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