Correct : a

The correct answer is Option C — The salesperson can make the trip on both networks (i) and (ii).
The salesperson''s trip is a Hamiltonian Cycle problem — a closed path that visits every city (vertex) exactly once and returns to the starting city. We check if such a cycle exists in each network.
Figure (i) — 4×4 Grid Network (16 cities): For a grid graph G(m×n), a Hamiltonian cycle exists if and only if m×n is even and both m ≥ 2, n ≥ 2. Here 4×4 = 16 (even) and both dimensions exceed 1. The Hamiltonian cycle exists.
Figure (ii) — Irregular 5-city Network: All 5 vertices have degree ≥ 2, and by tracing the edges a valid Hamiltonian cycle can be found — visiting all 5 cities exactly once before returning to the start.
Since a Hamiltonian cycle exists in both networks, the salesperson can complete the required trip on both highway systems.
Key distinction: this is a Hamiltonian cycle (every city visited once), not an Eulerian circuit (every road traversed once). For grid graphs, the even-vertex rule directly determines Hamiltonicity.