Question

Find x(g) for the graph.

Question 1 options:

1


2


3


4

Question 2 (1 point)

Find x(g) of the graph

Question 2 options:

2


3


4


5

Question 3 (1 point)

Below is a map of the Southeastern United States. What is the minimum number of colors required so that no two adjacent states have the same color?

Question 3 options:

2


3


4


5

Question 4 (1 point)

Given the graph, which vertex coloring is correct?

Question 4 options:

red (A, B, H); green (D, C, E); blue (G, F); yellow (I)


red (A, C, F); green (B, D, G); blue (E, H); yellow (I)


red (A, B, H); green (D, E, F); blue (C, G); yellow (I)


red (A, D, E, F); green (C, G); blue (B, H); yellow (I)

Question 5 (1 point)

The following is an appropriate color-map for the graph.

Question 5 options:

True. No adjacent vertex has the same color.


False. Adjacent vertices have the same color.


True. The Chromatic number is 4.


False. Purple and Orange should be switched on the inner star.

Answer 1

1. The x(g) is just the minimum number of colors needed to color the graph without a color being repeated. The answer is 2.

2. The minimum number needed to color this without repeating a color is 3.

3. The minimum number of colors required so that no two adjacent states have the same color is 3.

4. Remember, no colors can be repeated so options like A & B or D & E cannot be choices. The answer is is red (A, C, F); green (B, D, G); blue (E, H); yellow (I).

5. True. No adjacent vertex has the same color.