Hello,
You can define the tagged vlans you want to have between trunks ports and also you can define a Native vlan and permit it in the trunk avoiding the rest of the vlans (this way you avoid traffic from vlan 1), the question is Why do you want to avoid untagged traffic? there are control traffic that is not tagged and is important to be in your network. Other hand you can define the MAC address you want to access to a port, with the next commands (in access ports):
switchport port-security
switchport port-security mac-address type-mac-here
switchport port-security maximum 1
switchport port-security violation shutdown
This way the interface goes down when any other mac that try to connect to this port.
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Best Regards,