The concept of arithmetic-geometric index was recently introduced in chemical graph theory, but it has proven to be useful from both a theoretical and practical point view. aim this paper is obtain new bounds the characterize extremal graphs with respect them. Several are based on other indices, such as second variable Zagreb or general atom-bond connectivity index), some them involve parameter...

Let k ≥ 2 be an integer, a k-decomposition (G1,G2, . . . ,Gk) of the complete graph Kn is a partition of its edge set to form k spanning subgraphs G1,G2, . . . ,Gk. In this contribution, we investigate the Nordhaus–Gaddum-type inequality of a k-decomposition of Kn for the general Zagreb index and a 2-decomposition for the Zagreb co-indices, respectively. The corresponding extremal graphs are ch...

—The graphs which are used in this paper simple, finite and undirected. The first second Zagreb indices for every non-adjacent vertices (also called coindices) dependent only on the degrees interspersed operations of addition multiplication, respectively, vertices. number edges incident vertex v a graph G is degree two u if it’s no common edge between them. In paper, we found coindices chains e...

1 Karmela Aleksic-Maslac, University of Zagreb, Faculty of Electrical Engineering and Computing, Unska 3, Zagreb, Croatia, [email protected] 2 Branko Jeren, University of Zagreb, Faculty of Electrical Engineering and Computing, Zagreb, Croatia, [email protected] 3 Zvonko Kostanjcar (Student), University of Zagreb, Faculty of Electrical Engineering and Computing, Zagreb, Croatia, Zvonko.K...

A new extension of the generalized topological indices (GTI) approach is carried out to represent “simple” and “composite” topological indices (TIs) in an unified way. This approach defines a GTI-space from which both simple and composite TIs represent particular subspaces. Accordingly, simple TIs such as Wiener, Balaban, Zagreb, Harary and Randić connectivity indices are expressed by means of ...

We show how generalized Zagreb indices $M_1^k(G)$ can be computed by using a simple graph polynomial and Stirling numbers of the second kind. In that way we explain and clarify the meaning of a triangle of numbers used to establish the same result in an earlier reference.

A topological descriptor is regarded as a numerical parameter derived by using mathematical tools from the molecular graph of different chemical structures. The theory paramount section chemistry. In this section, there are many parameters, that have very useful characteristics to study structure chemicals. article, we investigate indices concealed non-kekulean benzenoid hydrocarbon graph. We w...

Let $G=(V,E)$, $V={v_1,v_2,ldots,v_n}$, be a simple graph with$n$ vertices, $m$ edges and a sequence of vertex degrees$Delta=d_1ge d_2ge cdots ge d_n=delta$, $d_i=d(v_i)$. Ifvertices $v_i$ and $v_j$ are adjacent in $G$, it is denoted as $isim j$, otherwise, we write $insim j$. The first Zagreb index isvertex-degree-based graph invariant defined as$M_1(G)=sum_{i=1}^nd_i^2$, whereas the first Zag...

In this paper we study lower bounds in a unified way for large family of topological indices, including the first variable Zagreb index M 1 ? . Our aim is to obtain sharp inequalities and characterize corresponding extremal graphs. The main results provide several vertex-degree-based indices. These are new even Zagreb, inverse forgotten