The author proposes that the following relations hold exactly for the lattice animal model of branched polymers. The resistivity exponent zeta a is exactly equal to da, the fractal dimensionality of the backbone of the anomals. The random walk fractal dimensionality dw is given by, dw=da+da, where da is the fractal dimensionality of the animals. The spectral dimension ds of the backbone of the animals is given by, ds=1 at all dimensions, i.e. the backbone is a highly decorated but essentially chain-like object. These are in contrast with earlier suggestions that one needs two (three) topological properties to obtain zeta a(dw). The author proposes that these relations may hold for all clusters for which loops are irrelevant and have a finite upper critical dimensionality. The implications of these results for diffusion-limited aggregates and percolation clusters are also discussed.