Existence of stable electronic energy levels in the presence of vibrational and off-diagonal disorder

We have found that the topological arrangement of atoms can guarantee the existence of stable electronic eigenvalues. These levels are stable in the presence of vibrational and off-diagonal disorder. Graph theory is used to describe the topological structure of the Hamiltonian. The actual applications are presented in tight-binding approximation. It was found that graph theory can be used even if the atoms have more than one atomic orbital.