[Discrete Maths] Graph Theory Rosen,Chromatic number

Question

What are the chromatic number of following graphs?

Answer is 6 and 4 respectively.But i am getting 3 for both.

Please someone confirm this?

Comments

The answer which you are getting is for EDGE CHROMATIC number NOT (vertex) CHROMATIC number..

Answer 1

Yes we can color both of them with 3 color so that no two same color is adjacent. but how can we sure that it is not less than 3. As both the graph consist triangle it can't be color with less than 3. So we at least require 3 color to color them.

Moreover they are planer graph, according to four color theorem : The chromatic number of a planar graph is no greater than four.
https://en.wikipedia.org/wiki/Four_color_theorem

Answer 2

yes both of them have 3 chromatic number

Answer 3

3 is the correct answer for both