  The $S=1$ antiferromagnetic Heisenberg model on a Kagome lattice is studied
using the density-matrix renormalization group method. To identify the ground
state, we take four kinds of clusters into account; periodic, cylindrical, and
two open ones. The hexagonal singlet solid (HSS) and triangular valence bond
solid (TVBS) states are artificially generated by modulating edge shapes of the
open clusters. We find that the energy par sites of the HSS state is $e_0=E_0/N
=-1.41095$, which is readily lower than that of the TVBS state ($e_0=-1.3912
\pm 0.0025$). This agrees well with those of the cylindrical ($e_0=-1.40988$)
and periodic ($e_0=-1.409 \pm 0.005$) clusters, where no assumption as to the
ordering is posed. Thus, we conclude that the HSS picture is consistent to
describe the ground state of the $S=1$ Kagome Heisenberg model. This is further
confirmed by finding non-symmetry-breaking state in the calculations of the
dimer-dimer correlation functions as well as the entanglement entropy of
cylindrical clusters. Finally, we estimate the single-triplet energy gap: The
HSS ground state has $\Delta=0.1919$, while the TVBS excited state has a larger
one $\Delta=0.2797$.
