On exactness of semidefinite programming relaxation for the maximum cut problem

Semidefinite programming provides a relaxation of the maximum cut problem on a graph. We investigate and present a few classes of graphs for which the semidefinite relaxation of the maximum cut problem is exact. For each of these classes, we determine the optimal objective value by explicitly constructing a maximum cut. Furthermore, we prove the uniqueness of the exact solution for two of these graph classes.