एक पूर्ण ग्राफ एक ऐसा ग्राफ होता है जिसमें शीर्षों के किसी भी युग्म के बीच एक जोड़ने वाला किनारा होता है। यह एक C++ प्रोग्राम है जो कंप्लीट ग्राफ पर एज कलरिंग करता है।
एल्गोरिदम
Begin Take the input of the number of vertices ‘n’. Construct a complete graph using e=n*(n-1)/2 edges, in ed[][]. Function EdgeColor() is used to Color the graph edges. A) Assign color to current edge as c i.e. 1 initially. B) If the same color is occupied by any of the adjacent edges, then discard this color and go to flag again and try next color. C) Print the color for each edge. End
उदाहरण
#include<iostream>
using namespace std;
void EdgeColor(int ed[][3], int e) {
int i, c, j;
for(i = 0; i < e; i++) {
c = 1; //assign color to current edge as c i.e. 1 initially.
flag:
ed[i][2] = c;
//If the same color is occupied by any of the adjacent edges, then
discard this color and go to flag again and try next color.
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]) {
c++;
goto flag;
}
}
}
}
}
int main() {
int i, n, e, j, cnt = 0;
cout<<"Enter the number of vertexes for the complete graph: ";
cin>>n;
e = (n*(n-1))/2;
int ed[e][3];
for(i = 1; i <= n; i++) {
for(j = i+1; j <= n; j++) {
ed[cnt][0] = i;
ed[cnt][1] = j;
ed[cnt][2] = -1;
cnt++;
}
}
EdgeColor(ed , e);
for(i = 0; i < e; i++)
cout<<"\nThe color of the edge between vertex
n1):"<<ed[i][0]<<" and n(2):"<<ed[i][1]<<" is: color"<<ed[i][2]<<".";
} आउटपुट
Enter the number of vertexes for the complete graph: 4 The color of the edge between vertex n(1):1 and n(2):2 is: color1. The color of the edge between vertex n(1):1 and n(2):3 is: color2. The color of the edge between vertex n(1):1 and n(2):4 is: color3. The color of the edge between vertex n(1):2 and n(2):3 is: color3. The color of the edge between vertex n(1):2 and n(2):4 is: color2. The color of the edge between vertex n(1):3 and n(2):4 is: color1.