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In this paper, we determine the unique maximum (or minimum) extremal graph for general spectral radius, zeroth-order general Randić index, general sum-connectivity index, general Platt index, second Zagreb index and multiplicative Zagreb indices in the class of cacti with n ≥ 4 vertices and k ≥ 0 cycles. By applying our new result, we demonstrate the unique maximum extremal graph for general spectral radius, zeroth-order general Randić index, general sum-connectivity index, general Platt index, second Zagreb index and second multiplicative Zagreb index in the class of cacti with n ≥ 4 vertices. Furthermore, we also determine the unified maximum extremal graphs for general spectral radius, zeroth-order general Randić index and the second multiplicative Zagreb index in the class of cacti with n ≥ 4 vertices and k ≥ 1 pendant vertices. [ABSTRACT FROM AUTHOR]