Question

A cycle on n vertices is isomorphic to its complement. The value of n is

• A. 5

Answer 1

The correct option is A 5
If a graph is isomorphic to its own complement then it is a self complementary graph. In a self complementary graph
$e=\frac{n(n-1)}{4}$

but in the cycle $C_n,e=n.$

Som if a cycle is self complementary, then
$n=\frac{n(n-1)}{4}$

The solution of the above equation is n = 5.

So, $C_5$ is the only cycle graph which is self complementary.