This question is about $$search$.$ There are three rooms and two robots, A and B$.$

Each room allows at most one robot at a time. We use $$O$$ to represent an empty room.

As a result, there are the following six states. It$$s a centralized system, and the operator

can move one robot $($A or B$)$ to the empty room at a time, resulting in two actions of

MovA and MovB respectively. The operator also has a $$switch$$ action to exchange the

positions of the two robots.

The costs of the MovA, MovB, and Switch actions are $2,3,$ and $6$ respectively. In case of a tie, actions are selected alphabetically $($MovA is evaluated first, and Switch is the last evaluated$).$ As an example, the operator can use the action sequence Switch$-$MovB to go from S$1$ to S$5.$

a$.$ Construct an undirected graph for this search problem. Label the states and actions