Your Answer is

Correct Answer is E

Explanation

According to the question stem, it can be known that each road must be walked once and only once, so it can be converted into a question of "drawing in one stroke". If the number of lines emanating from a point is odd, then this point is called a singularity. When the number of singular points in a graph is 0 or 2, the graph can be drawn in one stroke. There are 2 singular points in the question, so it needs to start from one singular point and end at another singular point, so only E is eligible.