Thanks for your reply but I tested with ctime and it also does not
change after a directory move/rename:

root@marty:/vol3# ls -lhc --full-time
drwxr-xr-x 2 root root 48 2006-02-16 15:24:17.000000000 -0500
test/

root@marty:/vol3# mv test test2

root@marty:/vol3# ls -lhc --full-time
drwxr-xr-x 2 root root 48 2006-02-16 15:24:17.000000000 -0500
test2/