Hence correct option is b with 4 colors.
<u>Step by-step explanation:</u>
We are given a graph in which we need to color every vertex or node such that no adjacent vertex or node should have the same color, ex:- If color of node B is blue than it's adjacent vertex A and D must not have the same blue color. Now, Let's start coloring of graph :
Color vertex A as red : Now, it's adjacent vertex as B,C,D,E must not have red color we know this!.
Color vertex B as blue: Now, it's adjacent vertex A and D must not have blue color!
Color vertex C as blue: Now, it's adjacent vertex A,E and D must not have blue color!
Color vertex D as green: Now, it's adjacent vertex A,B,C and E must not have green color!
Color vertex E as purple: Now, it's adjacent vertex C and D must not have purple color!
Hence correct option is b with 4 colors.
