Explanation:

To understand this question, let's first define what a cycle and its complement mean in the context of graph theory.

Definition: A cycle is a closed path in a graph where each vertex is connected to its adjacent vertices, and the last vertex is connected to the first vertex.

Definition: The complement of a graph is a graph that has the same set of vertices but with the edges that are not present in the original graph.

Now, let's consider a cycle with n vertices. We can represent this cycle as a set of vertices connected by edges in a circular manner.

For example, let's consider a cycle with 5 vertices:

A -- B -- C -- D -- E -- A

The complement of this graph would be a graph with the same set of vertices but with the edges that are not present in the original graph. In other words, if two vertices are connected in the original graph, they would not be connected in the complement graph, and vice versa.

Now, let's construct the complement graph for the cycle with 5 vertices:

A -- C
A -- D
A -- E
B -- D
B -- E
C -- E

As we can see, the complement graph is not isomorphic to the original graph. The complement graph has more edges and does not have the same connectivity pattern as the original graph.

Therefore, the statement "A cycle on n vertices is isomorphic to its complement" is not true for all values of n.

However, if we consider a cycle with 4 vertices, the complement graph would look like this:

A -- C
A -- D
B -- D

In this case, the complement graph is isomorphic to the original graph. The vertices are connected in the same pattern, just with different labels. Therefore, the value of n for which a cycle is isomorphic to its complement is 4.

Hence, the correct answer is option 'D' - 5.

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