jstree custom node markup

Is there a way to have custom markup or add additional html elements to some of the nodes.

For example, we want to add an arrow (link) right after the node text for all the nodes under a path, and when user click on the arrow, open the context menu. I know the context menu can be opened using the right click, but the requirement is to have an arrow after the node and clicking on the arrow should open the context menu.

Is there a way to customize or add additional html elements to selective tree nodes, and programmatically open the context menu or link click event.