Changes in the fast dynamics of polybutadiene (PB) with molecular weight and molecular architecture have been investigated by light and neutron scattering spectroscopy. Differences observed in the fast dynamics of various molecules correlate with differences seen in the value of the glass-transition temperature (T-g). The segmental and fast dynamics as well as the value of T-g are dependent on the total molecular weight of the molecule but independent of its architecture. In other words, the dynamics of PB depend on the number of segments in the molecule but do not show a significant dependence on how the segments are connected (molecular topology), even for arm molecular weights commensurate with the entanglement molecular weight. Literature data for the T-g's of highly branched, phenolic-terminated dendritic poly(benzyl ethers) of various core structures exhibit the same trend. There is no explanation for why the segmental motion appears to be sensitive to the total molecular weight of the molecule but is independent of its architecture.