only Question #5

Consider the necessary and sufficient conditions for the existence of an Euler circuit and path. Euler Circuit - A connected multigraph with at least two vertices has an Euler circuit if and only if each of its vertices has even degree. Euler Path - A connected multigraph has an Euler path but not an Euler circuit if and only if it has exactly two vertices of odd degree. 5. For which values of n do complete graphs Kn have an Euler circuit? 6. For which values of n do complete graphs Kn have an Euler path? 7. For which values of n do cycle graphs Cn have an Euler circuit? (Solution on page 2) 8. For which values of n do cycle graphs Cn have an Euler path? (Solution on page 2) 9. For which values of n do wheel graphs Wn have an Euler circuit? 10. For which values of n do wheel graphs Wn have an Euler path