A central question in the study of quantum many-body systems is the classification of quantum phases of matter, and one of the fundamental quantities for classifying a model's phase is whether or not it has a spectral gap above the ground state energy. In their seminal work, Affleck, Kennedy, Lieb and Tasaki introduced a family of spin-1 antiferromagnetic, isotropic spin chains, and showed that it satisfied the three properties of the Haldane phase, including a gap. Generalizations of this model to other lattices were also introduced. They conjectured that if the coordination number of a given regular, translation invariant lattice was sufficiently small, that the associated AKLT model would have a positive spectral gap. Otherwise, the model would exhibit Neel order and, hence, be gapless. Decorated versions of AKLT models obtained from replacing edges of lattices with chains of spin-1 particles have also been of interest, e.g., as their ground states constitute a universal quantum computation resource. A natural question, then, is whether or not decorated AKLT models belong to gapped or gapless ground state phases. In this talk, we consider AKLT models defined on decorated versions of (potentially infinite) simple, connected graphs and show that for sufficiently large decoration, the resulting model belongs to a gapped phase. In particular, the minimal decoration needed to ensure a gap only depends on the maximal vertex degree in the lattice. We then turn to the question of the stability of the spectral gap in the presence of small perturbations. In the case of the AKLT model on the decorated hexagonal model, we discuss how to use cluster expansion techniques to prove that the ground states are sufficiently indistinguishable so that spectral gap stability results in the spirit of Bravyi, Hastings and Michalakis hold.