Graph algorithms are widely used in several application domains. It has been established that parallelizing graph algorithms is challenging. The parallelization issues get exacerbated when graphics processing unit (GPU) is used to execute graph algorithms. In particular, three important GPU-specific aspects affect performance: memory coalescing, memory latency, and thread divergence. We attempt to tame these challenges using approximate computing. We target graph applications on GPUs that can tolerate some degradation in the quality of the output, in exchange for obtaining the result faster. We propose three techniques for boosting the performance of graph processing on the GPU by injecting approximations in a controlled manner. The first one creates a graph isomorph that brings relevant nodes nearby in memory and adds a controlled replica of nodes to improve coalescing. The second reduces memory latency by facilitating the processing of subgraphs inside shared memory by adding edges among specific nodes and processing well-connected subgraphs iteratively inside shared memory. The third technique normalizes degrees across nodes assigned to a warp to reduce thread divergence. Each technique offers notable performance benefits and provides a knob to control inaccuracy added to an execution. We demonstrate the effectiveness of the proposed techniques using a suite of large graphs with varied characteristics and five popular graph algorithms.