The Narumi–Katayama index of a graph G is equal to the product of the degrees of the vertices of G. In this paper we consider a new version of the Narumi– Katayama index in which each vertex degree d is multiplied d times. We characterize the graphs extremal w.r.t. this new topological index.

‎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 $n$-ve...

‎    The Narumi-Katayama index is the first topological index defined by the product of some graph theoretical quantities. Let G be a simple graph. Narumi-Katayama index of G is defined as the product of the degrees of the vertices of G. In this paper, we define the Narumi-Katayama polynomial of G. Next, we investigate some properties of this polynomial for graphs and then, we obtain ...

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) ...

‎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 $n$-ve...

The Narumi-Katayama index of a graph was introduced in 1984 for representing the carbon skeleton of a saturated hydrocarbons and is defined as the product of degrees of all the vertices of the graph. In this paper, we examine the Narumi-Katayama index of different total transformation graphs. MSC (2010): Primary: 05C35; Secondary: 05C07, 05C40