Is there an option on facebook to...?

[Kassan]

Is there an option you can enable which allows you to only log on from one desktop? Meaning when you enable the option, it would deny access to any other desktops from logging on my account?

[Terence]

Login approval is the option for you. Before that make sure your account is safe, from the Account Settings > Security page, look for ‘Active Sessions‘ and click on Edit.Now all previous sessions will be listed, together with the current active session at the top of the list. Click on the link ‘End Activity‘ to kill the activities from other devices.
Login approvals is an extended security feature offered by Facebook, and it will require you to enter a security code each time you try to access your Facebook account from unrecognized devices. To activate Login Approvals, go to Account Settings > Security, look for Login Approvals and click on the Edit button.An option to activate Login Approvals will appear, tick the check box to activate.A popup window will appear with descriptions of login approvals, click on the Set Up Now button to continue.