Augmented Zagreb Index Research Articles

The Edge Version of Degree Based Topological Indices of HAC5C6C7[p, q] Nanotube

Let G be a simple molecular graph with vertex set V (G) and edge set E(G) respectively. The degree deg(v) of the vertex v 2 V (G) is the number of vertices adjacent with vertex v. A graph can be recognized by a numeric number, a polynomial, a sequence of numbers or a matrix. A topological index is a numeric quantity associated with a graph which characterize the topology of graph and is invariant under graph automorphism. Topological indices play important role in mathematical chemistry especially in the quantitative structureproperty relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies. In this paper we compute the edge version of some important degree based topological indices like Augmented Zagreb Index, Hyper-Zagreb Index, Harmonic Index and Sum-Connectivity Index of HAC5C6C7[p; q] Nanotube.

The Augmented Zagreb Indices of Fluoranthene-Type Benzenoid Systems

The augmented Zagreb index (AZI index) of a graph $$G=(V,E)$$ , which is a valuable predictive index in the study of the heat of formation in octanes and heptanes, is defined as $$\begin{aligned} \hbox {AZI}(G)=\sum _{uv\in E(G)}\left( \frac{d_{u}d_{v}}{d_{u}+d_{v}-2}\right) ^{3}{,} \end{aligned}$$ where $$d_{u}$$ and $$d_{v}$$ are the degrees of the terminal vertices u and v of edge uv, respectively. In this paper, we give the expressions for computing the augmented Zagreb indices of fluoranthene-type benzenoid systems, and we determine the extremal values of augmented Zagreb index in f-benzenoid systems with h hexagons. Especially, we give the extremal values of augmented Zagreb index in cata-catacondensed fluoranthene-type benzenoid systems with h hexagons.

Bounds for the augmented Zagreb and the atom-bond connectivity indices

Using electrical networks and majorization we obtain a lower bound for the augmented Zagreb index in terms of the number of vertices and edges, and the maximum vertex degree. An analogous upper bound for the atom-bond connectivity index is also obtained. These bounds, which are attained by the complete graph Kn, are not comparable to the ones found in the literature.

The Edge Version of Degree Based Topological Indices of p NA<sub>q</sub><sup style="margin-left:-6px;">p</sup> Nanotube

Chemical graph theory is an important branch of mathematical chemistry which has wide range applications. In chemical graph theory a molecular graph can be recognized by a numerical quantity which is called a Topological index. Topological indices have some major classes but among these classes degree based topological indices have prominent role in chemical graph theory. In this paper we compute the edge version of some important degree based topological indices like Augmented Zagreb Index, Hyper-Zagreb Index, Harmonic Index and Sum-Connectivity Index of NAqp Nanotube.

Further Inequalities Between Vertex-Degree-Based Topological Indices

Continuing the recent work of L. Zhong and K. Xu [MATCH Commun. Math. Comput. Chem.71(2014) 627-642], we determine inequalities among several vertex-degree-based topological indices; first geometric-arithmetic index(GA), augmented Zagreb index (AZI), Randi$\acute{c}$ index (R), atom-bond connectivity index (ABC), sum-connectivity index (X)and harmonic index (H).

Computing Sanskruti index of certain nanostructures

Inspired by recent work of augmented Zagreb index (AZI) we propose here a new topological index, Sanskruti index\(\mathcal {S}(G)\) of a molecular graph G. In QSAR/QSPR study, topological indices are utilized to guess the bioactivity of chemical compounds. The Sanskruti index \(\mathcal {S}(G)\) shows good correlation with entropy of an octane isomers. In this paper we compute the Sanskruti index \(\mathcal {S}(G)\) of line graphs of subdivison graphs of 2D-lattice, nanotube and nanotorus of \(\textit{TUC}_{4}C_{8}[p,q]\).

Some results on topological indices of graphene

Graph theory has provided chemist with a variety of useful tools, such as topological indices. A topological index Top(G) of a graph G is a number with the property that for every graph H isomorphic to G, Top(H) = Top(G). In this article, we present exact expressions for some topological indices of carbon compound graphene. We compute first Zagreb index, second Zagreb index, first multiple Zagreb index, second multiple Zagreb index, augmented Zagreb index, harmonic index and hyper-Zagreb index of graphene. These are some topological indices based on degrees.

Unicyclic and bicyclic graphs with minimal augmented Zagreb index

The augmented Zagreb index of a graph G is defined as $$ \operatorname{AZI}(G)=\sum_{uv\in E(G)} \biggl( \frac{d_{u}d_{v}}{d_{u}+d_{v}-2} \biggr)^{3}, $$ where $E(G)$ is the edge set, and $d_{u}$ , $d_{v}$ are the degrees of vertices u and v in G, respectively. This new molecular structure descriptor, introduced by Furtula et al. (J. Math. Chem. 48:370-380, 2010), has proven to be a valuable predictive index in the study of the heat of formation in heptanes and octanes. In this paper, the n-vertex unicyclic graphs with the minimal and the second minimal AZI indices and the n-vertex bicyclic graphs with the minimal AZI index are determined.

Testing the quality of molecular structure descriptors. Vertex-degree-based topological indices

The correlation ability of 20 vertex-degree-based topological indices, occurring in the chemical literature, is tested for the case of standard heats of formation and normal boiling points of octane isomers. It is found that the correlation ability of many of these indices is either rather weak or nil. The augmented Zagreb index and the atom-bond connectivity index yield the best results.

Bond additive modeling 10. Upper and lower bounds of bond incident degree indices of catacondensed fluoranthenes

Bond incident degree index is a descriptor that is calculated as the sum of the bond contributions such that each bond contribution depends solely on the degrees of its incident vertices (e.g. Randić index, Zagreb index, modified Zagreb index, variable Randić index, atom-bond connectivity index, augmented Zagreb index, sum-connectivity index, many Adriatic indices, and many variable Adriatic indices). In this Letter we find tight upper and lower bounds for bond incident degree index for catacondensed fluoranthenes with given number of hexagons.

Augmented Zagreb index

Inspired by recent work on the atom-bond connectivity (ABC) index we propose here a new topological index, augmented Zagreb index (AZI). The tight upper and lower bounds for chemical trees are obtained. Moreover, it has been shown that among all trees the star has the minimum AZI value. Characterizing trees with maximal augmented Zagreb index remains an open problem for future research.