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This paper presents a novel concept of G-Hardy-Rogers functional operators on metric spaces endowed with a graph. It investigates sufficient circumstances under which such a mapping becomes a Picard operator. As applications of the principal idea discussed herein, a few important corresponding fixed point results in ordered metric spaces and cyclic operators are pointed out and analyzed. For upcoming research papers in this field, comparative graphical illustrations are created to highlight the pre-eminence of proposed notions with respect to the existing ones.