Program to check given Graph is tree or not

#include<iostream>
#include<list>
using namespace std;

class Graph
{
 int V,E;
 list<int> *adj;
 public:
  Graph()
  {
   cout<<endl<<"Enter the no of vertices and edges:";
   cin>>V>>E;
   
   adj=new list<int>[V];
   
   int v1,v2;
   for(int i=0;i<E;i++)
   {
    cout<<endl<<"Enter the vertices for edge "<<i+1<<"  :";
    cin>>v1>>v2;
    adj[v1].push_back(v2);
    adj[v2].push_back(v1);
   }
  }
  ~Graph()
  {
   delete []adj;
  }
  bool isCycle();
  bool isCyclicUtil(int v,bool visited[],int parent);
};

bool Graph::isCycle()
{
 bool* visited=new bool[V];
 
 for(int i=0;i<V;i++)
 visited[i]=false;
 
 if(isCyclicUtil(0,visited,-1))
 return false;
 
 for(int u=0;u<V;u++)
     if(!visited[u])
     return false;
   
 return true;
}

bool Graph::isCyclicUtil(int v,bool visited[],int parent)
{
    visited[v]=true; 
 
 list<int>::iterator it;
 for(it=adj[v].begin();it!=adj[v].end();++it)
 {
  if(!visited[*it])
  {
   if(isCyclicUtil(*it,visited,v))
   return true;
  }
  else
  if(*it!=parent)
  return true;
 }
 
 return false;
}

int main()
{
 Graph g;
 if(g.isCycle())
 cout<<endl<<"Given graph is a tree";
 else
 cout<<endl<<"Given graph is not a tree";
}