To determine the day of the week on May 28, 2006, we can use the concept of Zeller's Congruence. This formula allows us to calculate the day of the week for any given date.

Zeller's Congruence is as follows:
\[ h = \left(q + \frac{13(m+1)}{5} + K + \frac{K}{4} + \frac{J}{4} - 2J\right) \mod 7 \]

Where:
- h is the day of the week (0 = Saturday, 1 = Sunday, 2 = Monday, ..., 6 = Friday)
- q is the day of the month
- m is the month (3 = March, 4 = April, ..., 12 = December; January and February are counted as months 13 and 14 of the previous year)
- K is the year of the century (year % 100)
- J is the zero-based century (actually ⌊ year/100 ⌋)

Now let's calculate the day of the week for May 28, 2006, using Zeller's Congruence:

- q = 28
- m = 5 (May)
- K = 6 (2006 % 100 = 6)
- J = 20 (⌊ 2006/100 ⌋ = 20)

Substituting these values into the formula:
\[ h = \left(28 + \frac{13(5+1)}{5} + 6 + \frac{6}{4} + \frac{20}{4} - 2 \cdot 20\right) \mod 7 \]

Simplifying the equation:
\[ h = \left(28 + 12 + 6 + 1 + 5 - 40\right) \mod 7 \]
\[ h = 12 \mod 7 \]
\[ h = 5 \]

Since h = 5, the day of the week for May 28, 2006, is Friday. Therefore, option B is incorrect, and the correct answer is option D, Sunday.