  We study quantum entanglement in the ground state of the
Affleck-Kennedy-Lieb-Tasaki (AKLT) model defined on two-dimensional graphs with
reflection and/or inversion symmetry. The ground state of this spin model is
known as the valence-bond-solid state. We investigate the properties of reduced
density matrix of a subsystem which is a mirror image of the other one. Thanks
to the reflection symmetry, the eigenvalues of the reduced density matrix can
be obtained by numerically diagonalizing a real symmetric matrix whose elements
are calculated by Monte Carlo integration. We calculate the von Neumann entropy
of the reduced density matrix. The obtained results indicate that there is some
deviation from the naive expectation that the von Neumann entropy per valence
bond on the boundary between the subsystems is $\ln 2$. This deviation is
interpreted in terms of the hidden spin chain along the boundary between the
subsystems. In some cases where graphs are on ladders, the numerical results
are analytically or algebraically confirmed.
