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The multiplicative sum Zagreb index is a graph invariant defined as the product of the sums of the degrees of pairs of adjacent vertices in a graph. In this paper, we compute the multiplicative sum Zagreb index of some composite graphs such as splice graphs, bridge graphs, and bridge-cycle graphs in terms of the multiplicative sum Zagreb indices of their components. Then, we apply our results to compute the multiplicative sum Zagreb index for several classes of chemical graphs and nanostructures.

Multiplicative-sum Zagreb index of splice, bridge, and bridge-cycle graphs