Удаление вершины с графа

#include "stdafx.h"
#include<iostream>
#include<list>
using namespace std;

class Graph
{
    int V;    
    list<int> *adj;

    void DFSUtil(int v, bool visited[]);
public:
    Graph(int V);   
    void addEdge(int v, int w); 
    void DFS(int v); 
    void print();
    void deleteVertex(int v);
};
Graph::Graph(int V)
{
    this->V = V;
    adj = new list<int>[V];
}
void Graph::addEdge(int v, int w)
{
    adj[v].push_back(w); 
    adj[w].push_back(v);
}

void Graph::print() {
    for (int v = 0; v < V; v++) {
        cout << "List: " << v << endl;
        for (auto x : adj[v])
            cout << "-->" << x;
        cout << endl;
    }
}
void Graph::deleteVertex(int v)
{
    //adj[v].remove();
}

void Graph::DFSUtil(int v, bool visited[])
{
    visited[v] = true;
    cout << v << " ";
    list<int>::iterator i; 
    for (i = adj[v].begin(); i != adj[v].end(); ++i)
        if (!visited[*i])
            DFSUtil(*i, visited);
}

void Graph::DFS(int v)
{
    bool *visited = new bool[V];
    for (int i = 0; i < V; i++)
        visited[i] = false;
    DFSUtil(v, visited);
}
int main()
{
    int size;
    cout << "Enter count of Vertex" << endl;
    cin >> size;
    Graph g(size);
    int firstVertex, secondVertex;
    int answer = 1, i = 0;
    while (answer != 0 && i < size - 1) {
        i++;
        cout << "Enter conected Vertex: \n";
        cin >> firstVertex;
        cin >> secondVertex;
        cout << "Do you want to continue? 1 yes 0 - no" << endl;
        cin >> answer;
        cout << "\nCurrent i is" << i << endl;
        g.addEdge(firstVertex, secondVertex);
    }
    g.deleteVertex(2);
    g.DFS(0);
    cout << endl;
    g.print();
    return 0;
}

Как реализовать правильно функцию удаления вершины? Если возможно помогите кодом