A graph is self-complementary if it is isomorphic to its complement. For all self-complementary graphs on n vertices, \( n \) is _______.
Show Hint
- a multiple of 4
- even
- odd
- congruent to 0 mod 4 or 1 mod 4
The Correct Option is D
Solution and Explanation
For a graph to be self-complementary, the number of vertices \( n \) must be such that \( n \equiv 0 \, (\text{mod } 4) \) or \( n \equiv 1 \, (\text{mod } 4) \). This is a necessary condition for the graph and its complement to be isomorphic.
Therefore, the correct answer is option (4).
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