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Which of the following statements are correct?

  1. The complement of a simple disconnected graph must be connected.
  2. The complement of a simple connected graph must be disconnected.
  3. The complement of complete bipartite graph $\text{K}(4,6)$ has $10$ components.
  4. If $\text{G}$ is a self-complementary graph i.e. $\text{G}$ is isomorphic to its complement. Then $\text{G}$ must have $4k$ or $4k + 1$ vertices for some integer $k.$
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A is true. Below is the proof of it :



D is true because the number of edges in a self-complementary graph is as following :


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