An Isograft is a graft of tissue between two individuals who are genetically identical (i.e. monozygotic twins). Transplant rejection between two such individuals virtually never occurs.
As monozygotic twins have the same major histocompatibility complex, there is very rarely any rejection of transplanted tissue by the adaptive immune system. Furthermore, there is virtually no incidence of graft-versus-host disease. This forms the basis for why the preferred choice of a physician considering an organ donor will be a monozygotic twin.
In 1993 a research article demonstrated that islet isografts were being transplanted into young diabetic mice [STZ induced diabetic NOD mice] and the mice survived at least about 22 days post transplantation.