Polymer fiber or corresponding fabric including graphene and/or its derivative(s), wherein the graphene including polymer fabric is characterized by feature selected from the group consisting of anti-microbial, antistatic, wicking, thermal cooling, anti-odour, and ultraviolet protection, or any combination thereof. The graphene including polymer fiber or fabric shows several further beneficial properties including but not limited to good/excellent washing fastness, rubbing fastness, perspiration fastness, sublimation fastness, and light fastness. A process by which the graphene and/or its derivative(s) is incorporated in a polymer during its synthesis. The polymer is subsequently drawn into a fiber or fabric, and is capable of being converted into commercial products. A method to improve the aforementioned properties in a polymer fiber or fabric.