graph components

Question

Let G be the graph whose vertex is the set of K-tuples with elements in {0, 1}, with x adjacent to y, if x and y different in exactly two positions. The number of components of G _____

1.    1
2.    2
3.    3
4.    4

Comments

3 ??

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i got only 2.

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Consider k=3 the vertices will be {000,001,010,011,100,101,110,111}
We can separate these vertices into
A = {000, 011, 101, 110} (even number of 1’s)
B = {001, 010, 100, 111} (odd number of 1’s)
As shown in graph

Any vertex in A will never connects to any other vertex in B. A, B both forms two disconnected complete graphs 
Therefore, even with k size tuples we can divide them into two completely disconnected complete graphs.