In our modern world, environmental concerns have become paramount, with a particular focus on mitigating the release of harmful gases into the atmosphere. One such gas of significant concern is hydrogen sulfide (H₂S), known for its noxious odor and detrimental effects on both human health and the environment. This study delves into the crucial importance of removing H₂S from effluent gases before their release into the environment. We bridge existing knowledge gaps by investigating the adsorption of hydrogen sulfide on graphene sheets, utilizing advanced computational tools. Through detailed simulations, we explore various adsorption sites on the graphene surface, including top (T), bridge (B), and hollow (H) sites, to determine the most effective removal mechanisms. Most importantly, we carefully explore the impact of the adsorption sites present at the edge and center regions of the graphene surface. Our study reveals that there are significant differences in the adsorption strength of hydrogen sulfide across the sites present at the edge and surface regions of the graphene sheets, confirming that edge sites are more effective for hydrogen sulfide adsorption. The findings derived from our study not only contribute to a deeper understanding of hydrogen sulfide adsorption but also highlight the promising role of carboxylate-function-decorated graphene (via its edge and surface sites and functional group assessment) in environmentally friendly gas removal technologies.