A method for quickly calculating the Huckel molecular orbital eigenvalues and other properties of two series of open-ended single-walled nanotubes is given. Circumscribing generates series of related nanotubes and mirror-plane fragmentation and embedding of larger molecular graphs gives smaller sub graphs resulting in substantial simplification of eigenvalue calculations. Molecular graphs with greater than two-fold symmetry are at least doubly degenerate in about two-thirds of their Huckel molecular orbital eigenvalues and that the right-hand mirror-plane subgraphs only contains one set of these doubly degenerate eigenvalues. Recursion equations derived for the (5,0) nanotube series allow one to obtain eigensolutions for indefinitely large members. (C) 2016 Elsevier B.V. All rights reserved.