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For a (molecular) graph, the first multiplicative Zagreb index $\prod_1(G) $is the product of the square of every vertex degree, and the secondmultiplicative Zagreb index $\prod_2(G) $ is the product of the products ofdegrees of pairs of adjacent vertices. In this paper, we explore graphs interms of (edge) connectivity. The maximum and minimum values of $\prod_1(G) $and $\prod_2(G) $ of graphs with connectivity at most $k$ are provided. Inaddition, the corresponding extremal graphs are characterized, and our resultsextend and enrich some known conclusions.

On the sharp upper and lower bounds of multiplicative Zagreb indices of graphs with connectivity at most k