Automatically detect lightdm or gdm?

[quicksketch]

It looks like these scripts are identical other than the service restart command at the end of the script. If that's the case, shouldn't it be possible to simply detect the display manager and consolidate these two scripts into a single one?

eg:

DISPLAY_MANAGER = $(tail /etc/X11/default-display-manager);
if [[ $DISPLAY_MANAGER = *"gdm"* ]]; then
  service gdm restart;
elif [[ $DISPLAY_MANAGER = *"lightdm"* ]]; then
  service lightdm restart;
else
  echo "Unknown display manager."
fi