Question

Let G be the graph with V(G) = {1, 2, 3, 4, 5} and E(G) = {(1, 2), (2, 3), (2, 4), (3, 4), (4, 5), (5, 1), (1,4)}. Determine the number of colorings of G with m colors such that no two adjacent vertices have the same color.