To quickly identify whether a graph can be completed in one stroke, it is necessary to count the number of singularities in the graph (singularities, that is, the number of line segments passing through this point is odd). If the number of singularities is 0 or 2, the graph can be completed in one stroke, and vice versa.

Number of strokes = odd number divided by 2

Odd numbers are 0 and 2 are strokes.

When the odd number is even > 2, the number of strokes is divided by 2.

When the odd number is greater than 2 (3, 5, 7, 9 ...), divide by 2, and the result quotient+1 gets the number of strokes (because the remainder is even smaller! )。

For example, the number of singularities in a graph is 0 or 2 (singularities, points leading to odd lines).

According to the above two conditions, it can be judged that ① is not a connected graph, ④ has four singularities, and ⑤ has six singularities, all of which cannot be drawn with one stroke, while ② and ③ have 0 and 2 singularities, respectively, which can be drawn with one stroke.