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Manycore GPU architectures have become mainstay for accelerating graph computations. One of the primary bottlenecks to performance of graph computations on manycore architectures is the data movement. Since most of the accesses in graph processing are due to vertex neighborhood lookups, locality in graph data structures plays a key role in dictating the degree of data movement. Vertex reordering is a widely used technique to improve data locality within graph data structures. However, these reordering schemes alone are not sufficient as they need to be complemented with efficient task allocation on manycore GPU architectures to reduce latency due to local cache misses. Consequently, in this paper, we introduce a software/hardware co-design framework for accelerating graph computations. Our approach couples an architecture-aware vertex reordering with a priority-based task allocation technique. As the task allocation aims to reduce on-chip latency and associated energy, the choice of Network-on-Chip (NoC) as the communication backbone in the manycore platform is an important parameter. By leveraging emerging three-dimensional (3D) integration technology, we propose design of a small-world NoC (SWNoC)-enabled manycore GPU architecture, where the placement of the links connecting the streaming multiprocessors (SM) and the memory controllers (MC) follow a power-law distribution. The proposed 3D SWNoC-enabled software/hardware co-design framework achieves 11.1% to 22.9% performance improvement and 16.4% to 32.6% less energy consumption depending on the dataset and the graph application, when compared to the default order of dataset running on a conventional planar mesh architecture.