Final answer:
Cytotoxic T lymphocytes, which are involved in graft rejection and elimination of virus-infected cells, recognize and interact with Class I HLA molecules.
Step-by-step explanation:
The class of HLA molecules recognized by cytotoxic T lymphocytes, primarily involved in graft rejection and cell-mediated killing of virus-infected cells, is Class I HLA molecules. Cytotoxic T cells, also known as CD8+ T cells, have the primary role of identifying and destroying cells that are infected with intracellular pathogens, such as viruses. All nucleated cells in the body express Class I HLA molecules for presenting intracellular antigens. When these antigens are identified as abnormal or foreign, cytotoxic T cells are activated to kill the infected cells. Class I HLA molecules also play a significant role in organ transplant rejection; differences in MHC I molecules between donor and recipient can lead to the recognition of transplanted tissue as foreign and its subsequent rejection by the immune system.