Proved as follows:

Note that this graph consists of 8 points, and each point is the intersection of 3 edges.

For the convenience of the following description, we define this point as a node.

These three sides are defined as the degrees of nodes.

Each node has 3 degrees.

First prove that the node can only be the starting point or the end point of a pen.

Prove:

Suppose there is a node that is neither the end nor the starting point, we define it as the transition point.

Then, because it is not the starting point, it is required to be drawn, so you have to go through it to some extent.

Suppose there is a stroke from one direction to a point, because it is not the end point, so it must be.

Draw in a different direction and leave. For this reason, the degree of the transition point must be even.

So nodes can't be transition points.

According to the above reason, this topic consists of 8 nodes and needs 3 strokes, so there are at most 3 strokes.

Node is the starting point and three nodes are the end points, so at least two nodes should be transition points, but as mentioned above,

Nodes can't be transition points, and such a diagram can't be drawn three times without repetition.

If you don't understand or know anything, or find that I did something wrong, you are welcome to bring it up and we will discuss it together.