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