Finding a cycle path in directed graph - c++

Question

I am making a directed Graph class. I want find if there is any Cycle and update a vector with it's path accordingly. My Function some times work but others add two times the last edge of the path.So i guess it needs to be tydied up.
Example: having a Graph with these paths
0->1, 0->2, 1->2, 2->3, 3->4, 4->0, 4->6, 1->5, 5->6
should set the vector to [0 2 3 4] or anything else valid.
What I have tried:
#include <iostream>
#include <vector>
#include <list>
#include <algorithm>
using namespace std;
class Graph {
private:
int V;
list<int> *adj;
bool isCyclicHelp(int v, bool visited[], bool *rs, vector<int> &path) const{
if(visited[v] == false) {
visited[v] = true;
rs[v] = true;
list<int>::iterator i;
for(i=adj[v].begin(); i!=adj[v].end(); i++) {
if(!visited[*i] && isCyclicHelp(*i, visited, rs, path)) {
path.push_back(*i);
return true;
}
else if(rs[*i]) {
return true;
}
}
}
rs[v] = false;
path.pop_back();
return false;
}
public:
Graph(int V) {
this->V = V;
adj = new list<int>[V];
}
~Graph() {
}
void addEdge(int v, int w) {
if(v != w) {
adj[v].push_back(w);
}
}
bool cycle(vector<int> &path) const {
bool *visited = new bool[V];
bool *recStack = new bool[V];
for(int i=0; i<V; i++) {
visited[i] = false;
recStack[i] = false;
}
for(int i=0; i<V; i++) {
path.push_back(i);
if(Graph::isCyclicHelp(i, visited, recStack, path)) {
reverse(path.begin(), path.end());
return true;
}
path.clear();
}
path.clear();
return false;
}
};