  Temperley-Lieb algebras have been generalized to sl(3) web spaces. Since a
cubic bipartite planar graph with suitable directions on edges is a web, the
quantum sl(3) invariants naturally extend to all cubic bipartite planar graphs.
First we completely classify them as a connected sum of primes webs. We also
provide a method to find all prime webs and exhibit all prime webs up to 20
vertices. Using quantum sl(3) invariants, we provide a criterion which
determine the symmetry of graphs.
