_i$: subdivided stars $S$ with ${\mathcal{G}}(S)=i$ and $S$ is not in a previous class.  Figure \[fig:tabEquivSim0\] shows the equivalence classes of the subdivided stars.  (-0,0.0) - (-0,-0.0); (-0,0.0) - (0.0,0.0);  (0.00,0.0) node [Number of paths of length 0 in the subdivided star]{}; (-0.0,-0.0) node\[rotate=00\] [Number of paths in the subdivided star]{};  (-0.0,0) node [0]{}; (-0.0,-0) node [0]{}; (-0.0,-0) node [0]{}; (-0.0,-0) node [0]{}; (-0.0,-0) node [0]{}; (-0.0,-0) node [0]{}; (-0.0,-0) node [...]{}; (-0.0,-0) node [$0p$]{}; (-0.0,-0) node [$0p+0$]{};  (0,0.0) node [0]{}; (0,0.0) node [0]{}; (0,0.0) node [0]{}; (0,0.0) node [0]{}; (0,0.0) node [0]{}; (0,0.0) node [0]{}; (0,0.0) node [...]{}; (0,0.0) node [$0p$]{}; (0,0.0) node [$0p+0$]{};  (empty) at (0,0) [0]{}; (p0) at (0,0) [$0^*$]{};  (p0) at (0,-0) [$0^*$]{}; (p0) at (0,-0) [0]{};  (p0b) at (0,-0) [0]{}; (p0) at (0,-0) [$0^*$]{}; (p0) at (0,-0) [$0^*$]{};  (s000) at (0,-0) [