  For nonconvex quadratically constrained quadratic programs (QCQPs), we first
show that, under certain feasibility conditions, the standard semidefinite
(SDP) relaxation is exact for QCQPs with bipartite graph structures. The exact
optimal solutions are obtained by examining the dual SDP relaxation and the
rank of the optimal solution of this dual SDP relaxation under strong duality.
Our results on the QCQPs generalize the results on QCQP with sign-definite
bipartite graph structures, QCQPs with forest structures, and QCQPs with
nonpositive off-diagonal data elements. Second, we propose a conversion method
from QCQPs with no particular structure to the ones with bipartite graph
structures. As a result, we demonstrate that a wider class of QCQPs can be
exactly solved by the SDP relaxation. Numerical instances are presented for
illustration.
