# C++ Program to Solve the Dominating Set Problem

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This is a C++ program to solve the Dominating Set problem.

## Algorithm

Begin
Take the number of vertices and edges as input. Also take the edge point of the edges.
function dominant():
Declare vector Set.
Take any edge e graph connecting the vertices i.e.; X and Y.
Add one vertex between X and Y to set s.
Delete all the edges connected to X.
End

## Example

#include<bits/stdc++.h>
using namespace std;
vector<vector<int> > g;
bool visit;
int i,j;
vector<int> dominant(int v,int e) {
vector<int> Set;
//Take any edge e graph connecting the vertices i.e.; X and Y.
for(i=0;i<v;i++) {
if(!visit[i]) {
visit[i]=true;
for(j=0;j<(int)g[i].size();j++) {
if(!visit[g[i][j]]) {
visit[g[i][j]]=true;
break;
}
}
}
}
return Set;
}
int main() {
int v,e,a,b;
cout<<"Enter number of vertices:";
cin>>v;
cout<<"Enter number of Edges:";
cin>>e;
g.resize(v);
memset(visit,0,sizeof(visit)); //set all index value of an array as 0
for(i=0;i<e;i++) {
cout<<"Enter the end-points of edge "<<i+1<<" : ";
cin>>a>>b;
a--; b--;
g[a].push_back(b);
g[b].push_back(a);
}
vector<int> Set = dominant(v,e);
cout<<"The Dominant Set is:\n";
for(i=0;i<(int)Set.size();i++)
cout<<Set[i]+1<<" ";
return 0;
}

## Output

Enter number of vertices:7
Enter number of Edges:6
Enter the end-points of edge 1 : 1 2
Enter the end-points of edge 2 : 2 2
Enter the end-points of edge 3 : 3 4
Enter the end-points of edge 4 : 4 5
Enter the end-points of edge 5 : 6 7
Enter the end-points of edge 6 : 4 5
The Dominant Set is:
1 3 5 6