Rendezvous search on a star graph with examination costs

We discuss some of the problems that arise when two teams attempt to rendezvous on a star graph while minimizing a cost arising from three components: movement, time and searching. The intuitive strategy is to meet at the center, but in some circumstances this strategy is not optimal and the participants must employ the alternative strategy of meeting at a node. There is also the question of what tactics to employ on the first move. We derive procedures by which two participants can arrive at an optimal solution.