You must add the child if the parent is selected the left mouse button.
Advised to connect to the signal model
void activated ( const QModelIndex & index )
but the child was not added to what was the reason?
Slot is not called.
.cpp
Qt Code: 
  1. #include "mainwindow.h"
  2. #include "ui_mainwindow.h"
  3. #include "addfile.h"
  4. #include "addModel.h"
  5. MainWindow::MainWindow(QWidget *parent) :
  6.     QMainWindow(parent),
  7.     ui(new Ui::MainWindow)
  8. {
  9.     ui->setupUi(this);
  10.     model=new QStandardItemModel(0,4);
  11.    ui->treeView->setModel(model);
  12.    ui->treeView->setSelectionMode(QAbstractItemView::SingleSelection);
  13.    ui->treeView->setSelectionBehavior(QAbstractItemView::SelectRows);
  14.     QDomDocument docDoc;
  15.     QFile file("BDwww.xml");
  16.      if (!file.open(QIODevice::ReadOnly))
  17.     {
  18.      if (!docDoc.setContent(&file)) {
  19.          QDomElement domElemNode= docDoc.documentElement();
  20.          readFile(domElemNode);
  21.      }
  22.          file.close();
  23.      }
  24.  }
  25. MainWindow::~MainWindow()
  26. {
  27.     delete ui;
  28. }
  29. void MainWindow::changeEvent(QEvent *e)
  30. {
  31.     QMainWindow::changeEvent(e);
  32.     switch (e->type()) {
  33.     case QEvent::LanguageChange:
  34.         ui->retranslateUi(this);
  35.         break;
  36.     default:
  37.         break;
  38.     }
  39. }
  40. // Создание формы для добавления ссылки
  41. void MainWindow::on_pushButton_clicked()
  42. {
  43.     QFrame *messAdd_www = new QFrame;
  44.     messAdd_www->setWindowFlags(Qt::Tool | Qt::FramelessWindowHint);
  45.     messAdd_www->setGeometry(QRect(QPoint(QCursor::pos().x(), QCursor::pos().y()), QSize(250, 250)));
  46.     messAdd_www->setFrameStyle(QFrame::WinPanel | QFrame::Raised);
  47.     messAdd_www->setLineWidth(2);
  48.     closeButton= new QPushButton ("Closse",messAdd_www);
  49.     closeButton->setGeometry(120,180,90,30);
  50.     addButton=new QPushButton(tr("Add"),messAdd_www);
  51.     addButton->setGeometry(20,180,90,30);
  52.     linkWWW= new QLineEdit(messAdd_www);
  53.     messAdd_www->show();
  54. [COLOR="red"]connect(ui->treeView, SIGNAL(activated(const QModelIndex&)), this, SLOT(addChild(const QModelIndex&))); [/COLOR]//      THERE NOT WORKING
  55. connect(addButton,SIGNAL(clicked()),messAdd_www,SLOT(close()));
  56. connect(closeButton,SIGNAL(clicked()),messAdd_www,SLOT(close()));
  57. }
  58. // Создание формы для добавления категории
  59. void MainWindow::on_pushButton_2_clicked()
  60. {
  61.  QFrame *categoryAdd = new QFrame;
  62.  categoryAdd->setWindowFlags(Qt::Tool | Qt::FramelessWindowHint);
  63.  categoryAdd->setGeometry(QRect(QPoint(QCursor::pos().x(), QCursor::pos().y()), QSize(250, 250)));
  64.  categoryAdd->setFrameStyle(QFrame::WinPanel | QFrame::Raised);
  65.  categoryAdd->setLineWidth(2);
  66.  closeCategory= new QPushButton ("Closse",categoryAdd);
  67.  closeCategory->setGeometry(120,180,90,30);
  68.  addCategory=new QPushButton(tr("Add"),categoryAdd);
  69.  addCategory->setGeometry(20,180,90,30);
  70.  nameCategory= new QLineEdit(categoryAdd);
  71.  categoryAdd->show();
  72.   connect(addCategory,SIGNAL(clicked()),this,SLOT(appendixCategory()));
  73.  connect(addCategory,SIGNAL(clicked()),this,SLOT(addInFile()));
  74.  connect(addCategory,SIGNAL(clicked()),categoryAdd,SLOT(close()));
  75.  connect(closeCategory,SIGNAL(clicked()),categoryAdd,SLOT(close()));
  76. }
  77. void MainWindow::on_tabWidget_currentChanged(QWidget* )
  78. {
  79. }
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.h
Qt Code: 
  1. #define ADDMODEL_H
  2. #include "mainwindow.h"
  3. // Добавление потомка в категорию
  4. void MainWindow::appendixWWW(const QModelIndex&)
  5. {
  6. qDebug()<<"Slot activ";
  7.     childItem = new QStandardItem();
  8.     childItem->setText(linkWWW->text());
  9.     parentItem->setChild(0,childItem);
  10. }
  11. //Добавление категории в модель
  12. void MainWindow::appendixCategory()
  13. {
  14.     parentItem = new QStandardItem();
  15.     parentItem->setText(nameCategory->text());
  16.     model->setItem(model->rowCount(),0, parentItem);
  17. }
  18. // Второй вариант добавления потомка
  19. void MainWindow::addChild(const QModelIndex&)
  20. {
  21.     qDebug()<<"Slot activ";
  22.     QModelIndex index = ui->treeView->selectionModel()->currentIndex();
  23.     QAbstractItemModel *model = ui->treeView->model();
  24.     if (model->columnCount(index) == 0) {
  25.         if (!model->insertColumn(0, index))
  26.         {
  27.             return;
  28.         }
  29.     }
  30.     if (!model->insertRow(0, index))
  31.     {
  32.         return;
  33.     }
  34.     for (int column = 0; column < model->columnCount(index); ++column)
  35.     {
  36.         QModelIndex child = model->index(0, column, index);
  37.         model->setData(child, QVariant("[No data]"), Qt::EditRole);
  38.         if (!model->headerData(column, Qt::Horizontal).isValid())
  39.         {
  40.             model->setHeaderData(column, Qt::Horizontal, QVariant("[No header]"),Qt::EditRole);
  41.         }
  42.     }
  43. }
  44. #endif // ADDMODEL_H
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I've tried, and so the same problem slot is not called.
Qt Code: 
  1. connect(ui->treeView->selectionModel(),SIGNAL(selectionChanged(const QItemSelection&, const QItemSelection&)), this, SLOT(addChild(const QItemSelection&,const QItemSelection&)));
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P.S: Sorry for the mistakes! I'm Russian.