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 = \{v_۱,\ldots‎, ‎v_n \} and d(v) be‎ ‎the degree of vertex v in the graph G‎. ‎The Narumi-Katayama ‎index is defined as NK(G) = \prod_{v\in 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.

کلیدواژه ها:

Narumi-Katayama index ، ‎ ‎Molecular graph ، Clique number ، Independent number ، ‎Dendrimers.‎