एक अप्रत्यक्ष ग्राफ़ G का लाइन ग्राफ़ एक अन्य ग्राफ़ L(G) है जो G के किनारों के बीच आसन्नता का प्रतिनिधित्व करता है। इस कार्यक्रम में, हम एक इनपुट ग्राफ़ के लाइन ग्राफ़ में एज कलरिंग करते हैं।
एल्गोरिदम
Begin Take the input of the number of vertices ‘n’ and number of edges ‘e’. Take the input of ‘n’ vertex pairs for the ‘e’ edges in the graph in ed[][]. Function GenLineGraph(): Construct a line graph in LineEd[][]. To construct line graph, for each edge in the given graph, connect it to its adjacent edge in LineEd. Function EdgeColor(): Color the graph edges of LineEdge[][] graph. Assign color to current edge as col i.e. 1 initially. If any of the adjacent edges have the same color, then discard this color and go to flag again and try next color. Print the color for each edge of the line graph. End.
उदाहरण कोड
#include<iostream>
using namespace std;
int GenLineGraph(int ed[][2], char LineEd[][3], int e) {
int i, cnt = 0, j, N;
char c;
for(i = 0; i < e; i++) {
for(j = i+1; j < e; j++) {
if(ed[j][0] == ed[i][0] || ed[j][0] == ed[i][1] || ed[j][1] == ed[i][0] || ed[j][1] == ed[i][1]) {
LineEd[cnt][0] = 'a'+i;
LineEd[cnt][1] = 'a'+j;
LineEd[cnt][2] = 0;
cnt++;
}
}
}
N = cnt;
cout<<"\n\nThe adjacency list representation for the given graph: ";
for(i = 0; i < e; i++) {
cnt = 0;
c = 'a'+i;
cout<<"\n\t"<<c<<"-> { ";
for(j = 0; j < N; j++) {
if(LineEd[j][0] == i+'a') {
cout<<LineEd[j][1]<<" ";
cnt++;
} else if(LineEd[j][1] == i+'a') {
cout<<LineEd[j][0]<<" ";
cnt++;
} else if(j == e-1 && cnt == 0)
cout<<"Isolated Vertex!";
}
cout<<" }";
}
return N;
}
void EdgeColor(char ed[][3], int e) {
int i, col, j;
for(i = 0; i < e; i++) {
col = 1;
flag:
ed[i][2] = col;
for(j = 0; j < e; j++) {
if(j == i)
continue;
if(ed[j][0] == ed[i][0] || ed[j][0] == ed[i][1] || ed[j][1] == ed[i][0] || ed[j][1] == ed[i][1]) {
if(ed[j][2] == ed[i][2]) {
col++;
goto flag;
}
}
}
}
}
int main() {
int i, n, e, j, max = -1;
char c= 'a';
cout<<"Enter the number of vertices of the graph: ";
cin>>n;
cout<<"Enter the number of edges of the graph: ";
cin>>e;
int ed[e][2];
char LineEd[e*e][3];
for(i = 0; i < e; i++) {
cout<<"\nEnter the vertex pair for edge '"<<c++<<"'";
cout<<"\nV(1): ";
cin>>ed[i][0];
cout<<"V(2): ";
cin>>ed[i][1];
}
e = GenLineGraph(ed, LineEd, e);
EdgeColor(LineEd , e);
for(i = 0; i < e; i++)
cout<<"\nThe color of the edge between vertex n(1):"<<LineEd[i][0]<<" and n(2):"<<LineEd[i][1]<<" is: color"<<0+LineEd[i][2]<<".";
} आउटपुट
Enter the number of vertices of the graph:4
Enter the number of edges of the graph: 3
Enter the vertex pair for edge 'a'
V(1): 1
V(2): 2
Enter the vertex pair for edge 'b'
V(1): 3
V(2): 2
Enter the vertex pair for edge 'c'
V(1): 4
V(2): 1
The adjacency list representation for the given graph:
a-> { b c }
b-> { a }
c-> { a }
The color of the edge between vertex n(1):a and n(2):b is: color1.
The color of the edge between vertex n(1):a and n(2):c is: color2.