タブを閉じる

<Button
    Content="Close the selected tab"
    Command="{x:Static igWindows:TabControlCommands.CloseSelected}"
    CommandTarget="{Binding ElementName=xamTabControl1}" />
<igWindows:XamTabControl Name="xamTabControl1" AllowTabClosing="True">
    <igWindows:TabItemEx Header="Tab 1">
        <!--TODO: ここでコンテンツを追加します-->
    </igWindows:TabItemEx>
    <igWindows:TabItemEx Header="Tab 2">
        <!--TODO: ここでコンテンツを追加します-->
    </igWindows:TabItemEx>
    <igWindows:TabItemEx Header="Tab 3">
        <!--TODO: ここでコンテンツを追加します-->
    </igWindows:TabItemEx>
</igWindows:XamTabControl>

Imports Infragistics.Windows.Controls
...
Me.xamTabControl1.ExecuteCommand(TabControlCommands.CloseSelected)
...

using Infragistics.Windows.Controls;
...
this.xamTabControl1.ExecuteCommand(TabControlCommands.CloseSelected)
...