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Question

A graph is self-complementary if it is isomorphic to its complement. For all self-complementary graphs on n vertices, n is

A
A multiple of 4
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B
Even
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C
Odd
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D
Congruent to 0 mod 4, or 1 mod 4
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Solution

The correct option is D Congruent to 0 mod 4, or 1 mod 4
An n-vertex self-complementary graph has exactly half number of edges of the complete graph i.e. n(n1)4~edges.

Since n(n - 1) must be divisible by 4, n must be congruent to 0 mod 4 or 1 mod 4.

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