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For a molecular graph, the first multiplicative Zagreb index $\Pi_1$ is equalto the product of the square of the degree of the vertices, while the secondmultiplicative Zagreb index $\Pi_2$ is equal to the product of the endvertexdegree of each edge over all edges. Denote by $\mathbb{G}_{n,k}$ the set ofgraphs with $n$ vertices and $k$ cut edges. In this paper, we explore graphs interms of a number of cut edges. In addition, the maximum and minimummultiplicative Zagreb indices of graphs with given number of cut edges areprovided. Furthermore, we characterize graphs with the largest and smallest$\Pi_1(G)$ and $\Pi_2(G)$ in $\mathbb{G}_{n,k}$, and our results extend andenrich some known conclusions.

On the maximum and minimum multiplicative Zagreb indices of graphs with given number of cut edges