Consider the image below:
###### Inspired by Settlers of Catan

Imagine you were playing a two-player game that involves each player taking turns draw a dot on one of the vertices of this graph. The rules for where a player can draw a dot are as follows:

A player can only draw a dot on a vertex that has not already been drawn on.

A player cannot draw a dot adjacent to another dot.

The game ends when a player is unable to place another dot. What is the minimum number of dots that can be placed in one complete game?

**Bonus:** can you generalize this for all other centered hexagonal boards?

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