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.© BrainMass Inc. brainmass.com July 23, 2018, 1:41 pm ad1c9bdddf
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 ...
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.