Question

The figure shows four road networks. Which of these four road networks can be traversed by a traveller, such that: 
- The traveller must cover all the roads in the network. 
- She may visit a city more than once, but she cannot travel on any road more than once. 
- She must come back to the city where she starts.

• A. A
• B. B
• C. C
• D. D

Hint:

For path traversal puzzles, always check degrees of vertices. If all vertices have even degrees → Eulerian circuit exists; if exactly two vertices have odd degrees → Eulerian path exists; otherwise → not possible.

Answer 1

The Correct Option is C

Step 1: Recall Euler’s circuit rule.
For a graph to allow a closed trail covering every edge exactly once (Eulerian circuit): - Every vertex must have an even degree. Step 2: Check each network.
- (A): Contains vertices of odd degree (e.g., Delhi, Mathura). Not Eulerian.
- (B): Also has multiple vertices of odd degree. Not Eulerian.
- (C): All cities have even degrees (2 or 4). Thus Eulerian circuit is possible.
- (D): Contains cities of odd degree (e.g., Guwahati). Not Eulerian.
Step 3: Conclude.
Therefore, only network (C) satisfies the conditions for Eulerian traversal. Final Answer: \[ \boxed{\text{C}} \]