Minimum Laplacian Controllability Problem of Lobsters

The lobster graph is a typical air-air communication network for UAVs with dozens to hundreds of individuals. Due to the existence of multiple eigenvalues, it is difficult to find out their minimum set of leaders. A new concept named Minimum Perfect Critical Set(MPCS) is proposed to solve the minimum Laplacian controllability problem. Some MPCSs are found for Lobsters. Based on these theories, an example shows that the minimum set of leaders can be found quickly.