Graph Help - Discrete Math !enter image description here The vertices indicate where cashiers are located; the edges denote unblocked aisles between cashiers. The department store wants to set up a security system where (plainclothes) guards are placed at certain cashier locations so that each cashier either has a guard at his or her location or is only one aisle away from a cashier who has a guard. What is the smallest number of guards needed? It seems there are 3 guards needed. They should be posted at (a,i,g) as far as I can tell. Anybody have a better idea?

Converting my comment to an answer ...

The maximum degree at any vertex is $3$, so any one guard watches at most $4$ cashiers. Thus, two guards aren't enough to watch $11$ cashiers. Your $3$-guard solution is therefore optimal ... but not unique: for instance, $(c, d, j)$ also works.