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 $v = {v_1,ldots‎, ‎v_n }$ and $d(v)$ be‎ ‎the degree of vertex $v$ in the graph $g$‎. ‎the narumi-katayama ‎index is defined as $nk(g) = prod_{vin v}d(v)$‎. ‎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.