The Graph Coloring Problem (GCP) is a significant optimization challenge widely suitable to solve scheduling problems. Its goal is to specify the minimum colors (k) required to color a graph properly. Due to its NP-completeness, exact algorithms become impractical for graphs exceeding 100 vertices. As a result, approximation algorithms have gained prominence for tackling large-scale instances. In this context, the Cat Swarm algorithm, a novel population-based metaheuristic in the domain of swarm intelligence, has demonstrated promising convergence properties compared to other population-based algorithms. This research focuses on designing and implementing the Cat Swarm algorithm to address the GCP. By conducting a comparative study with established algorithms, our investigation revolves around quantifying the minimum value of k required by the Cat Swarm algorithm for each graph instance. The evaluation metrics include the algorithm's running time in seconds, success rate, and the mean count of iterations or assessments required to reach a goal.