8.8:

6: Since G has triangles, chi is at least 3. One can do it with 3:
 a -> 1
 b -> 2
 c -> 1
 d -> 2
 e -> 1
 f -> 2
 g -> 3
   So chi =3.

"7": Use deletion/contraction on the edge (ab). Contraction leads to a
     triangle with double edge, whose chromatic polynomial is that of
     a triangle=K_3, which is n(n-1)(n-2) as discussed in class.
     Erasing the edge leads to a triangle with a dangling edge. The
     triangle can be colored in n(n-1)(n-2) ways, and the dangling
     vertex can be colored in (n-1) ways, because it can't replicate
     the color of vertex d. Hence chi_G(n) is 
     n(n-1)(n-2)(n-1) - n(n-1)(n-2) = n(n-1)(n-2)(n-2).
     For example, using 3 colors there are 6 ways. Choosing first a
     color for b, 3 choices here, one can then only choose from 2
     colors for d, and then everything is determined.