We investigate the topological constraints (entanglements) and dynamics of monodisperse polymer melts in the presence of a single wall carbon nanotube (SWCNT) in comparison to inclusion-free polymer melts by molecular dynamics simulations. The SWCNT has an infinite aspect ratio and radius smaller than the polymer radius of gyration. In the presence of SWCNT with or without attractive interactions, the contour length of the primitive path increases indicating more entanglements. We also find that there is a large heterogeneity in the polymer dynamics due to the polymers in contact with the SWCNT. The overall polymer diffusion decreases compared to its melt value and is affected by the enthalpic interaction between monomeric units and SWCNT, and the SWCNT radius. Moreover, the polymer chain diffusivity perpendicular to SWCNT is less than that parallel to the SWCNT in the entangled polymer systems where there is attraction between polymers and SWCNT surface. In the absence of SWCNT-polymer attractions, the polymer diffusion retains its melt value.