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Self-complementary graph proof

1.10 Let G be a self-complementary graph of order n, where n=1(mod 4)
Prove that G contains at least one vertex of degree (n-1)/2
(hint: Prove the stronger result that G contains an odd number of vertices of degree (n-1)/2.

Can you explain it step by step and draw a graph.

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This is a proof regarding a self-complementary graph.