- Isotropic Heisenberg models with nearest-neighbor interactions between spins located at the vertices of a bipartite (or alternant) graph are considered. Six theorems helping characterize the ground state are given. Building upon the theorems of Lieb and Mattis concerning the "nodelessness" of the wave functions and their spin symmetry, we establish related results concerning certain expectation values and "point group" symmetries. Applications especially concerning valence-bond descriptions of the -electron systems of organic molecules, are briefly indicated. 1982 American Institute of Physics.