Known errors and clarifications in For All Practical Purposes, 8th Edition Chapter 1 Skills Check #15. One set of teams never plays teams from the other set of teams. Therefore, the teams are probably divided into distinct leagues. Chapter 1 Skills Check #19. If a vertex has a valence of zero, no one chose that course. Chapter 1 Exercises #3a. According to the definition in this book, the loop prevents this figure from being considered a graph. However, other graph theory texts and examples in class do consider this figure to be a graph. Chapter 2 Skills Check #16. The answer should be 8.