# Graph coloring; chromatic number of graph

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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.

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##### 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.

##### 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 ...

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- AB, Hood College
- PhD, The Catholic University of America
- PhD, The University of Maryland at College Park

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