[Graph Theory (Miscellaneous)]

Several Top Secret Objects are connected by an underground railway in such a way that each Object is directly connected to no more than three others, and from each Object, it is possible to reach any other by underground travel with no more than one transfer. What is the maximum number of Top Secret Objects?

#
Evaluation. From this Object, you can reach three Objects in one "move", and with a transfer - to another $2 \cdot 3=6$ Objects. Therefore, there are no more than 10 Objects.

An example with 10 Objects is shown in the figure.

![](https://cdn.mathpix.com/cropped/2024_05_06_fee37b59e268953b86a9g-06.jpg?height=312&width=326&top_left_y=2468&top_left_x=869)

## Task