If you add to view the graphs as part of the dashboard,it would make sense to change tabs by making the other "fade out" instead of moving the unused tab on the right
"Fade out" in my world means making something invisible either by dimming it or making it more and more transparent. This "fade out" effect usually happens over a short period of time, so that you see the transformation.
Do you mean that actually selected tab should be highlighted in some way so that it stands out a little bit?