The 1:1 relationship is a relatively rare, but useful, type of relationship. It is the relationship where one parent record is associated with at most one child record.
The classic 1:1 example is the spousal relationship. It is really arbitrary whether the males or the females are designated as the parent-side of the relationship. The basic rule that must be enforced is the same: Bigamy is illegal.
How would you represent this in a database? If SSN is the primary key of the male and female tables, then the spousal relationship could be represented by storing the SSN of each person's spouse. This would be a foreign key pointing from each person to their spouse. For sake of example, let's designate the females as the parents and the males as the children. Then we would store the wife's SSN for each male.
How would you prevent two males from identifying the same female as their current spouse? You would create a secondary index on the foreign key field (WifeSSN) and restrict it to not allow any duplicates.
The relationship between departments and department heads at UT (and in most organizations) is also 1:1. Every department needs to have one boss and every employee can be the boss of at most one department.
How would you represent this in a database? First, you need to decide which table will be designated as the parent and which as the child. It is arbitrary in this example, but I suspect most of us would consider the department to be the parent of the employee. If you agree, then we should store the primary key of the department table (say, DeptID) as a foreign key in the employee table. For example, if Mary Jones is the head of the Accounting department, then we would store Acc as the value of her foreign key. If John Smith is an employee, but not the head of a department, then his foreign key would be null (missing).
How would you prevent two employees from identifying themselves as the boss of the same department? You would create an index on the foreign key field and restrict it to not allowing any duplicates.
The alternative approach is to store the primary key of the employee (say, SSN) as a foreign key in the department table. Again, if Mary Jones (123-45-6789) is the Accounting department boss, then 123-45-6789 would be stored as the foreign key for the Accounting record. Of course, we could store the 1:1 relationship both ways, but that would be redundant.