Question

Find the edge chromatic numbers of

1. 
2. 

Short answer

The edge chromatic numbers will be

a)

b)

Step-by-step solution

Given Information.

We have

1. 
2. 

Definition of Edge chromatic numbers

The edge chromatic numbers, sometimes alsocalled the chromatic index, of a graph is the fewest number of colors necessary to color each edge of. such that no two edges incident on the same vertex have the same color.

Solution (a)

We know that in any cycle, one color is not enough to color

In an even cycle we can take second color of the edge and the we will get absolute coloring.In an odd cycle we can take second color but we will be required another color to color the final edge.

Then

Solution (b)

In the wheel, there are ‘n’ spokes and all are adjacent , ‘n’ no. of color will be required to color them.

So,

The final solution is

1. 
2.