By default, when you open a sub-tree, you have to click on the little triangle on the left.
Is it possible to change the click behavior so that you can click anywhere on the name? Technically, this is really how about make the <li></li> element clickable that same way the icon is clickable.
You can set your jstree to do this when you init the jstree. In your select_node event for the node type you want to expand when clicked use the following:
For example:
Any nodes that are of type root will expand when clicked, while any nodes you have marked as default will be selected.