GATE 2015 CSE Graph Theory Questions

Question-1. 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
(b) Even
(c) odd
(d) Congruent to 0 mod 4, or, 1 mod 4
solution-1. A self-complementary graph of n vertices must have half number of edges than the complete graph corresponding to it. A complete graph has n*(n-1)/2 edges. So, a self-complementary graph would have n*(n-1)/4 edges.
If n is 0 mod 4, clearly, n*(n-1)/4 will be satisfied. for e.g. n=4,8... If n is 1 mod 4, for e.g. 5,9... the equation will be satisfied.
So correct option - (d)