Let G be a graph with vetex set V (G) and edge set E(G). The first generalizedfor a real number c > 0, and the second multiplicative Zagreb index is 2are the degrees of the vertices of u, v. The multiplicative Zagreb indices have been the focus of considerable research in computational chemistry dating back to Narumi and Katayama in 1980s. In this paper, we generalize Narumi-Katayama index and the first multicative index, where c = 1, 2, respectively, and extend the results of Gutman to the generilized tree, the k-tree, where the results of Gutman are for k = 1. Additionally, we characterize the extremal graphs and determine the exact bounds of these indices of k-trees, which attain the lower and upper bounds.
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