Chapter 14.2, Problem 3E

Euler Circuits In Exercises 1-3, a graph is shown and some sequences of vertices are specified. Determine which of these sequences show Euler circuits. If not, explain why not.

(a) $\text{A}\to \text{B}\to \text{C}\to \text{D}\to \text{E}\to \text{F}\to \text{A}$

(b) $\text{A}\to \text{B}\to \text{C}\to \text{D}\to \text{E}\to \text{G}\to \text{C}\to \text{E}\to \text{F}\to \text{G}\to \text{B}\to \text{F}\to \text{A}$

(c) $\text{A}\to \text{B}\to \text{C}\to \text{D}\to \text{E}\to \text{C}\to \text{G}\to \text{E}\to \text{F}\to \text{G}\to \text{E}\to \text{F}\to \text{A}$

(d) $\text{A}\to \text{B}\to \text{G}\to \text{E}\to \text{D}\to \text{C}\to \text{G}\to \text{F}\to \text{B}\to \text{C}\to \text{E}\to \text{F}\to \text{A}$