On computing the general Narumi-Katayama index of some graphs

The Narumi-Katayama index was the first topological index defined by the product of some graph theoretical quantities. Let G be a simple graph with vertex set V = {v1, . . . , vn} and d(v) be the degree of vertex v in the graph G. The Narumi-Katayama index is defined as NK(G) = ∏ v∈V d(v). In this paper, the Narumi-Katayama index is generalized using a n-vector x and it is denoted by GNK(G, x) for a graph G. Then, we obtain some bounds for GNK index of a graph G by terms of clique number and independent number of G. Also we compute the GNK index of splice and link of two graphs. Finally, we use from our results to compute the GNK index of a class of dendrimers.