A graph which has the same number of edges as its complement must have

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Module 5: Graphs and Trees

20222m

A graph which has the same number of edges as its complement must have number of vertices congruent to ______ or ______ modulo 4 (for integral values of number of edges).

(i) $6k, 6k-1$
(ii) $4k, 4k+1$
(iii) $k, k+2$
(iv) $2k+1, k$

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