We obtained the wheel $W_{n}$ when we add an additional vertex to the cycle $C_{n}$, for n>= 3. This means that wheel graph $W_{n}$ have all the vertices present in cycle graph $C_{n}$ and one additional vertex present at the center. This center vertex is connected to other all vertices. So wheel graph $W_{n}$ will have n + 1 vertices.
Here in the image, In $W_{4}$ we can see that all its edges are colored with 4 colors such that no two adjacent edges have the same color. It can't be colored with less than 4 colors because the center vertex is connected to 4 vertices and the edges which connected the center vertex to all the other vertices are adjacent. So we required at least 4 colors.
For $C_{n}$ it is easy to see that.
when n is even, we require 2 colors.
When n is odd, we require 3 colors.
For $K_{n}$ (complete graph),
As a vertex is connected to all other n-1 vertices. We at least require n - 1 colors but when we try to color all its edges with n-1 colors, we see that it can't be done with n-1 colors, We require at least n color to color the edges of the complelete graph.