Extremal augmented Zagreb index of trees with given numbers of vertices and leaves

Dutch windmill graph [1, 2] and denoted by Dnm. Order and size of Dutch windmill graph are (n−1)m+1 and mn respectively. In this paper, we computed certain topological indices and polynomials i.e. Zagreb polynomials, hyper Zagreb, Redefined Zagreb indices, modified first Zagreb, Reduced second Zagreb, Reduced Reciprocal Randi´c, 1st Gourava index, 2nd Gourava index, 1st hyper Gourava index, 2nd hyper Gourava index, Product connectivity Gourava index, Sum connectivity Gourava index, Forgotten index, Forgotten polynomials, M-polynomials and some topological indices in term of the M-polynomials i.e. 1st Zagreb index, 2nd Zagreb index, Modified 2nd Zagreb, Randi´c index, Reciprocal Randi´c index, Symmetric division, Harmonic index, Inverse Sum index, Augmented Zagreb index for the semitotal-point graph and line graph of semitotal-point graph for Dutch windmill graph.

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On Computation Degree-Based Topological Descriptors for Planar Octahedron Networks

Journal of Mathematics ◽

10.1155/2021/4880092 ◽

2021 ◽

Vol 2021 ◽

pp. 1-12

Author(s):

Wang Zhen ◽

Parvez Ali ◽

Haidar Ali ◽

Ghulam Dustigeer ◽

Jia-Bao Liu

Keyword(s):

Graph Theory ◽

Chemical Compound ◽

Topological Index ◽

Molecular Graph ◽

Topological Descriptors ◽

Zagreb Index ◽

Chemical Graph ◽

Symmetric Division ◽

Chemical Graph Theory ◽

Augmented Zagreb Index

A molecular graph is used to represent a chemical molecule in chemical graph theory, which is a branch of graph theory. A graph is considered to be linked if there is at least one link between its vertices. A topological index is a number that describes a graph’s topology. Cheminformatics is a relatively young discipline that brings together the field of sciences. Cheminformatics helps in establishing QSAR and QSPR models to find the characteristics of the chemical compound. We compute the first and second modified K-Banhatti indices, harmonic K-Banhatti index, symmetric division index, augmented Zagreb index, and inverse sum index and also provide the numerical results.

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Maximal augmented Zagreb index of trees with given diameter

Applied Mathematics and Computation ◽

10.1016/j.amc.2020.125855 ◽

2021 ◽

Vol 395 ◽

pp. 125855

Author(s):

Yisheng Jiang ◽

Mei Lu

Keyword(s):

Zagreb Index ◽

Augmented Zagreb Index

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Topological Indices of Certain Transformed Chemical Structures

Journal of Chemistry ◽

10.1155/2020/3045646 ◽

2020 ◽

Vol 2020 ◽

pp. 1-7 ◽

Cited By ~ 1

Author(s):

Xuewu Zuo ◽

Jia-Bao Liu ◽

Hifza Iqbal ◽

Kashif Ali ◽

Syed Tahir Raza Rizvi

Keyword(s):

Carbon Nanotube ◽

Line Graph ◽

Topological Indices ◽

Connectivity Index ◽

Zagreb Index ◽

Harmonic Index ◽

Chemical Structures ◽

Augmented Zagreb Index ◽

Carbon Nanotube Networks ◽

Atom Bond

Topological indices like generalized Randić index, augmented Zagreb index, geometric arithmetic index, harmonic index, product connectivity index, general sum-connectivity index, and atom-bond connectivity index are employed to calculate the bioactivity of chemicals. In this paper, we define these indices for the line graph of k-subdivided linear [n] Tetracene, fullerene networks, tetracenic nanotori, and carbon nanotube networks.

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Maximal Augmented Zagreb Index of Trees With at Most Three Branching Vertices

IEEE Access ◽

10.1109/access.2019.2946131 ◽

2019 ◽

Vol 7 ◽

pp. 146652-146661 ◽

Cited By ~ 1

Author(s):

Roberto Cruz ◽

Juan Daniel Monsalve ◽

Juan Rada

Keyword(s):

Zagreb Index ◽

Augmented Zagreb Index

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Expected Values of Some Molecular Descriptors in Random Cyclooctane Chains

Symmetry ◽

10.3390/sym13112197 ◽

2021 ◽

Vol 13 (11) ◽

pp. 2197

Author(s):

Zahid Raza ◽

Muhammad Imran

Keyword(s):

Molecular Descriptors ◽

Saturated Hydrocarbon ◽

Molecular Graph ◽

Chemical Compounds ◽

Total Surface Area ◽

Single Bond ◽

Zagreb Index ◽

Augmented Zagreb Index ◽

Explicit Formulae ◽

Expected Values

The modified second Zagreb index, symmetric difference index, inverse symmetric index, and augmented Zagreb index are among the molecular descriptors which have good correlations with some physicochemical properties (such as formation heat, total surface area, etc.) of chemical compounds. By a random cyclooctane chain, we mean a molecular graph of a saturated hydrocarbon containing at least two rings such that all rings are cyclooctane, every ring is joint with at most two other rings through a single bond, and exactly two rings are joint with one other ring. In this article, our main purpose is to determine the expected values of the aforementioned molecular descriptors of random cyclooctane chains explicitly. We also make comparisons in the form of explicit formulae and numerical tables consisting of the expected values of the considered descriptors of random cyclooctane chains. Moreover, we outline the graphical profiles of these comparisons among the mentioned descriptors.

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Sharp Bounds on the Augmented Zagreb Index of Graph Operations

Kragujevac Journal of Mathematics ◽

10.46793/kgjmat2004.509d ◽

2020 ◽

Vol 44 (4) ◽

pp. 509-522

Author(s):

N. DEHGARDI ◽

H. ARAM

Keyword(s):

Simple Graph ◽

Connectivity Index ◽

Regular Graphs ◽

Zagreb Index ◽

Sharp Bounds ◽

Graph Operations ◽

Degree Of A Vertex ◽

Augmented Zagreb Index ◽

Composition Product ◽

Product Of Graphs

Let G be a ﬁnite and simple graph with edge set E(G). The augmented Zagreb index of G is ( ) ∑ dG (u )dG (v) 3 AZI (G ) = ---------------------- , dG (u ) + dG (v) − 2 uv∈E(G ) where dG(u) denotes the degree of a vertex u in G. In this paper, we give some bounds of this index for join, corona, cartesian and composition product of graphs by general sum-connectivity index and general Randić index and compute the sharp amount of that for the regular graphs.

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