Code:
#include iostream
using namespace std;
// A function to generate line graph from a given graph.
int GenerateLineGraph(int edge[][2], char LineEdge[][3], int e)
{
int i, count = 0, j, NOV;
char ch;
// Loop to assign a valid color to every edge 'i'.
for(i = 0; i < e; i++)
{
for(j = i+1; j < e; j++)
{
// 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])
{
LineEdge[count][0] = 'a'+i;
LineEdge[count][1] = 'a'+j;
LineEdge[count][2] = 0;
count++;
}
}
}
NOV = count;
// Print the adjacency list representation of the graph.
cout<<"\n\nThe adjacency list representation for the given graph: ";
for(i = 0; i < e; i++)
{
count = 0;
// For each vertex print, its adjacent vertex.
ch = 'a'+i;
cout<<"\n\t"<
for(j = 0; j < NOV; j++)
{
if(LineEdge[j][0] == i+'a')
{
cout<
count++;
}
else if(LineEdge[j][1] == i+'a')
{
cout<
count++;
}
else if(j == e-1 && count == 0)
cout<<"Isolated Vertex!";
}
cout<<" }";
}
return NOV;
}
// A function to color edges of the graph.
void EdgeColoring(char edge[][3], int e)
{
int i, col, j;
// 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;
}
}
}
}
}
int main()
{
int i, v, e, j, max = -1;
char ch = 'a';
// 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][2];
char LineEdge[e*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 '"<
cout<<"\nV(1): ";
cin>>edge[i][0];
cout<<"V(2): ";
cin>>edge[i][1];
}
// Generate line graph.
e = GenerateLineGraph(edge, LineEdge, e);
// Color The line graph.
EdgeColoring(LineEdge , e);
// Print the color of edges of line graph.
for(i = 0; i < e; i++)
cout<<"\nThe color of the edge between vertex V(1):"<
}
Output:
Case 1:
Enter the number of vertexes of the graph: 4
Enter the number of edges of the graph: 5
Enter the vertex pair for edge 'a'
V(1): 1
V(2): 2
Enter the vertex pair for edge 'b'
V(1): 2
V(2): 3
Enter the vertex pair for edge 'c'
V(1): 3
V(2): 4
Enter the vertex pair for edge 'd'
V(1): 4
V(2): 1
Enter the vertex pair for edge 'e'
V(1): 1
V(2): 3
The adjacency list representation for the given graph:
a-> { b d e }
b-> { a c e }
c-> { b d e }
d-> { a c e }
e-> { a b c d }
The color of the edge between vertex V(1):a and V(2):b is: color1.
The color of the edge between vertex V(1):a and V(2):d is: color2.
The color of the edge between vertex V(1):a and V(2):e is: color3.
The color of the edge between vertex V(1):b and V(2):c is: color2.
The color of the edge between vertex V(1):b and V(2):e is: color4.
The color of the edge between vertex V(1):c and V(2):d is: color1.
The color of the edge between vertex V(1):c and V(2):e is: color5.
The color of the edge between vertex V(1):d and V(2):e is: color6.
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