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Graph coloring; chromatic number of graph

The three questions are stated in an attached .doc file (1.doc).

In part 1, a diagram is given, and whether the object depicted in the diagram is a graph is to be determined.

In part 2, a graph is given and its chromatic number is to be determined.

In part 3, a graph is given and the number of colors needed to color the regions of the graph (to ensure that adjacent regions have different colors) is to be determined.

Attachments

Solution Preview

Complete solutions are given in an attached .doc file (1-Solution.doc).

In part 1, it is determined that the objected depicted in the given diagram is a graph; its vertex set and edge set are presented.

In part 2, the definition of chromatic ...

Solution Summary

The question of whether the object depicted in the given diagram in part 1 is a graph is answered. A detailed determination of the chromatic number of the graph in part 2 is presented, as is a detailed determination of the number of colors needed in part 3 (to ensure that adjacent regions have different colors). The definition of chromatic number of a graph is reviewed.

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