Key strategies for solving discrete math graph theory problems include understanding the concepts of graph complements, isomorphic graphs, and self-complementary graphs. It is essential to calculate the number of unordered pairs of vertices in a graph and apply this to determine the edges in the complement of a graph. Drawing graphs to visualize relationships and ensuring that transformations maintain isomorphism are crucial steps in problem-solving. Additionally, constructing explicit bijections can help prove properties like self-complementarity in specific graph configurations. Engaging with each problem individually and demonstrating effort in understanding the underlying principles will enhance problem-solving skills.