  Let G be a graph with vertex set V (G) and edge set E(G). The first
generalized multiplicative Zagreb index of G is M_1(G) and the second
multiplicative Zagreb index is M_2(G). 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 multiplicative index, where c = 1, 2, respectively, and
extend the results of Gutman to the generalized 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.
