  We consider the spectral gap question for AKLT models defined on decorated
versions of simple, connected graphs G. This class of decorated graphs, which
are defined by replacing all edges of $G$ with a chain of $n$ sites, in
particular includes any decorated multi-dimensional lattice. Using the Tensor
Network States (TNS) approach from a work by Abdul-Rahman et. al. 2020, we
prove that if the decoration parameter is larger than a linear function of the
maximal vertex degree, then the decorated model has a nonvanishing spectral gap
above the ground state energy.
