A cycle on $n$ vertices is isomorphic to its complement. The value of $n$ is $\underline{\hspace{1cm}}$.

A cycle graph $C_n$ on $n$ vertices has $n$ edges.

The complete graph $K_n$ on $n$ vertices has $\frac{n(n-1)}{2}$ edges.

The complement of the cycle graph, denoted $\overline{C_n}$, has:

If a graph is isomorphic to its complement ($C_n \cong \overline{C_n}$), they must have the same number of edges:

Since $n \ge 3$ for a simple cycle graph:

For $n = 5$, the complement of $C_5$ is also a 5-cycle ($C_5$), hence $C_5$ is self-complementary.