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The emerging Ray-tracing cores on GPUs have been repurposed for non-ray-tracing tasks by researchers recently. In this paper, we explore the benefits and effectiveness of executing graph algorithms on RT cores. We re-design breadth-first search and triangle counting on the new hardware as graph algorithm representatives. Our implementations focus on how to convert the graph operations to bounding volume hierarchy construction and ray generation, which are computational paradigms specific to ray tracing. We evaluate our RT-based methods on a wide range of real-world datasets. The results do not show the advantage of the RT-based methods over CUDA-based methods. We extend the experiments to the set intersection workload on synthesized datasets, and the RT-based method shows superior performance when the skew ratio is high. By carefully comparing the RT-based and CUDA-based binary search, we discover that RT cores are more efficient at searching for elements, but this comes with a constant and non-trivial overhead of the execution pipeline. Furthermore, the overhead of BVH construction is substantially higher than sorting on CUDA cores for large datasets. Our case studies unveil several rules of adapting graph algorithms to ray-tracing cores that might benefit future evolution of the emerging hardware towards general-computing tasks.