1. **State the problem:** We have buses traveling between three Dzongkhags: Thimphu, Paro, and Wangdue. We need to first create a directed graph (digraph) showing bus routes (part i), and then calculate the total number of one-stopover trips from Thimphu to Paro (part ii). 2. **Create the digraph:** - Nodes are the Dzongkhags: Thimphu, Paro, Wangdue. - Directed edges represent bus routes with weights as the number of buses: - Thimphu \(\to\) Paro with weight 1 - Thimphu \(\to\) Wangdue with weight 2 - Paro \(\to\) Thimphu with weight 1 - Paro \(\to\) Wangdue with weight 1 - Wangdue \(\to\) Thimphu with weight 1 - Wangdue \(\to\) Paro with weight 1 3. **Calculate one-stopover trips from Thimphu to Paro:** - One-stopover means traveling from Thimphu to some Dzongkhag \(X\) and then from \(X\) to Paro. - Possible \(X\) values are the other Dzongkhags besides Thimphu and Paro, i.e., Wangdue, but also Paro itself if considered (though a direct route to Paro is not a stopover). - Routes via Wangdue: - From Thimphu to Wangdue: 2 buses - From Wangdue to Paro: 1 bus - Total one-stopover trips from Thimphu to Paro via Wangdue = \(2 \times 1 = 2\) 4. **Summary:** - Digraph nodes and edges correctly represent the data - The total number of one-stopover trips from Thimphu to Paro is 2 **Final answer:** $$\text{Number of one-stopover trips from Thimphu to Paro} = 2$$