This document summarizes research on parallelizing the graceful graph labeling problem using OpenMP on multi-core processors. It introduces the concepts of parallelization, multi-core architecture, and OpenMP. An algorithm is designed to parallelize graceful labeling by distributing graph vertices across processor cores. Execution time and speedup are measured for graphs of increasing size, showing improved speedup and reduced time with parallelization. Results show consistent performance gains as graph size increases due to better utilization of the multi-core architecture.