  Tests of the integrality properties of a scalar operator in topological
strings on a resolved conifold background or orientifold of conifold
backgrounds have been performed for arborescent knots and some non-arborescent
knots. The recent results on polynomials for those knots colored by SU(N) and
SO(N) adjoint representations are useful to verify Marino's integrality
conjecture up to two boxes in the Young diagram. In this paper, we review the
salient aspects of the integrality properties and tabulate explicitly for an
arborescent knot and a link. In our knotebook website, we have put these
results for over 100 prime knots available in Rolfsen table and some links. The
first application of the obtained results, an observation of the Gaussian
distribution of the LMOV invariants is also reported.
