Exercise 18.
Decide whether the following statements are true or false. Prove your answers.
If two graph \(G_1\) and \(G_2\) have the same chromatic number, then they are isomorphic.
If two graphs \(G_1\) and \(G_2\) have the same number of vertices and edges and have the same chromatic number, then they are isomorphic.
If two graphs are isomorphic, then they have the same chromatic number.