  Using the Matrix Product State framework, we generalize the
Affleck-Kennedy-Lieb-Tasaki (AKLT) construction to one-dimensional spin liquids
with global color ${\rm SU}(N)$ symmetry, finite correlation lengths, and edge
states that can belong to any self-conjugate irreducible representation (irrep)
of ${\rm SU}(N)$. In particular, ${\rm SU}(2)$ spin-$1$ AKLT states with edge
states of arbitrary spin $s=1/2,1,3/2,\cdots$ are constructed, and a general
formula for their correlation length is given. Furthermore, we show how to
construct local parent Hamiltonians for which these AKLT states are unique
ground states. This enables us to study the stability of the edge states by
interpolating between exact AKLT Hamiltonians. As an example, in the case of
spin-$1$ physical degrees of freedom, it is shown that a quantum phase
transition of central charge $c = 1$ separates the Symmetry Protected
Topological (SPT) phase with spin-$1/2$ edge states from a topologically
trivial phase with spin-$1$ edge states. We also address some specificities of
the generalization to ${\rm SU}(N)$ with $N>2$, in particular regarding the
construction of parent Hamiltonians. For the AKLT state of the ${\rm SU}(3)$
model with the $3$-box symmetric representation, we prove that the edge states
are in the $8$-dimensional adjoint irrep, and for the ${\rm SU}(3)$ model with
adjoint irrep at each site, we are able to construct two different
reflection-symmetric AKLT Hamiltonians, each with a unique ground state which
is either even or odd under reflection symmetry and with edge states in the
adjoint irrep. Finally, examples of two-column and adjoint physical irreps for
${\rm SU}(N)$ with $N$ even and with edge states living in the antisymmetric
irrep with $N/2$ boxes are given, with a conjecture about the general formula
for their correlation lengths.
