Apex domains cannot have CNAME records.
Question and response
Question
dig cs.purdue.edu. NS
Answer
cs.purdue.edu. 5 NS harbor.ecn.purdue.edu.
cs.purdue.edu. 5 NS ns1.rice.edu.
cs.purdue.edu. 5 NS ns2.rice.edu.
cs.purdue.edu. 5 NS ns3.purdue.edu.
cs.purdue.edu. 5 NS ns4.purdue.edu.
cs.purdue.edu. 5 NS pendragon.cs.purdue.edu.
Authority
The response has no authority records.
Additional
ns3.purdue.edu. 5 A 128.210.224.226
ns4.purdue.edu. 5 A 128.210.224.234
ns3.purdue.edu. 5 AAAA 2001:18e8:800:200:0:0:0:a
ns4.purdue.edu. 5 AAAA 2001:18e8:800:201:0:0:0:a
. 0 OPT ; payload 1232, xrcode 0, version 0, flags 0