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.
