1. **Problem Statement:** We are given a graph with cities A, B, C, D, E, X connected by flight routes with given weights. We need to determine which of the given flight paths is a Hamiltonian circuit. 2. **Definition:** A Hamiltonian circuit is a path in a graph that visits each vertex exactly once and returns to the starting vertex. 3. **Check each option:** - a. X C A D C X: Visits X, C, A, D, then C again before returning to X. Vertex C is visited twice, so this is not a Hamiltonian circuit. - b. A B C D E X A: Visits A, B, C, D, E, X, and returns to A. All vertices are visited exactly once and the path returns to the start. This fits the definition of a Hamiltonian circuit. - c. B A D E X A D: Visits B, A, D, E, X, A, D. Vertices A and D are visited twice, so this is not a Hamiltonian circuit. - d. A B C D E X: Visits A, B, C, D, E, X but does not return to the starting vertex A, so this is not a circuit. 4. **Conclusion:** The only Hamiltonian circuit among the options is **b. A B C D E X A**. Final answer: **b. A B C D E X A**