Magnetic properties of spin-1 antiferromagnetic chains with bond alternation Masayuki Hagiwara,∗1,∗2,∗3 Yasuo Narumi,∗3 Koichi Kindo,∗3 Masanori Kohno,∗4 Hiroki Nakano,∗5 Ryutaro Sato,∗6 and Minoru Takahashi∗7 ∗1Magnetic Materials Laboratory, RIKEN ∗2Faculty of Integrated Science, Yokohama City University ∗3Research Center for Materials Science at Extreme Conditions, Osaka University ∗4Mitsubis...

‎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 G is equal to the product of degrees of all the vertices of G. In this paper, we examine the NarumiKatayama index of some derived graphs such as a Mycielski graph, subdivision graphs, double graph, extended double cover graph, thorn graph, subdivision vertex join and edge join graphs.

The Narumi-Katayama index of a graph G, denoted by NK(G), is equal to the product of the degrees of the vertices of G. In this paper we compute this index for Splice and Link of two graphs. At least with use of Link of two graphs, we compute this index for a class of dendrimers. With this method, the NK index for other class of dendrimers can be computed similarly.

Let G be a graph with vetex set V (G) and edge set E(G). The first generalized multiplicative Zagreb index of G is ∏ 1,c(G) = ∏ v∈V (G) d(v) , for a real number c > 0, and the second multiplicative Zagreb index is ∏ 2(G) = ∏ uv∈E(G) d(u)d(v), where d(u), d(v) are the degrees of the vertices of u, v. The multiplicative Zagreb indices have been the focus of considerable research in computational ...

Abstract In this paper, with the aid of Faà di Bruno formula and by virtue properties Bell polynomials second kind, authors define a kind notion degenerate Narumi numbers polynomials, establish explicit formulas for derive (degenerate) Cauchy numbers.