Question

A cycle on n vertices is isomorphic to its complement. What is the value of n?

(a) 5

(b) 32

(c) 17

(d) 8

This question was posed to me in quiz.

My question comes from Isomorphism in Graphs in division Graphs of Discrete Mathematics

Answer 1

Correct answer is (a) 5

The best explanation: A cycle with n vertices has n edges. Number of edges in cycle = n and number of edges in its complement = (n*(n−1)/2) – n. To be isomorphism, both graphs should have equal number of edges. This gives, (n*(n-1)/2) – n = n

⇒ n = 5