Exercise 3.

Find the chromatic number of each of the following graphs.

A graph with five vertices arranged in a diamond with one vertex in the middle. The top vertex is connected to the two outside vertices below it, which are connected to the bottom vertex. The center vertex is connected to the two vertices to its left and right.
The graph C7: seven vertices arranged in a circle with edges connecting neighboring vertices (creating a 7-sided polygon).
Five vertices in a pentagon with a sixth vertex in the center. Edges form the outside of the pentagon, and the center vertex is adjacent to each outside vertex.
The graph K5: five vertices each adjacent to all the others, arranged in a pentagon.
The Petersen graph: ten vertices arranged in two rings of five each. Each outer vertex is adjacent to the two outer vertices closest to it, forming a pentagon, and to the inner vertex closest to it. Each inner vertex is adjacent to the two inner vertices not neighboring it, forming a 5-ponted star.
Solution.
in-context