🔧 Why is Hamiltonian graph?

    Graph();

    bool data_input(const std::string file_name); 

    void create_A(); 
    bool hamilton(int curr);

    void data_output(const std::string file_name); 
    void no_way_answer(const std::string file_name); 
    void error_output(const std::string file_name); 

    ~Graph();

bool Graph::data_input(const string file_name) { 

    int tek;
    ifstream in_file;
    in_file.open(file_name);

    if (in_file) { 
        if (in_file >> n && n>0) {
            while (!in_file.eof()) {
                if(in_file >> tek && tek>0)
                Vert.push_back(tek);
                else return false;
            }
        }
        else return false;
    }
    else return false;
    in_file.close();

    return true;
};

bool Graph::hamilton(int curr)
{
    Path.push_back(curr);

    if (Path.size() == n)
        return true;

    Visited[curr] = true;

    for (int nxt = 0; nxt < n; ++nxt) {
        if (A[curr][nxt] == 1 && !Visited[nxt])
            if (hamilton(nxt)) return true;
    }
    Visited[curr] = false;
    Path.pop_back();

    return false;
};

void Graph::error_output(const string file_name) { 

    ofstream errorFile;
    errorFile.open(file_name);

    errorFile << "Error";

    errorFile.close();
}