scholarly journals On atom-bond connectivity molecule structure descriptors

2016 ◽  
Vol 81 (3) ◽  
pp. 271-276 ◽  
Author(s):  
Boris Furtula ◽  
Ivan Gutman ◽  
Kinkar Das
Keyword(s):  
Molecular Structure ◽  
Connectivity Index ◽  
Benzenoid Hydrocarbons ◽  
Molecule Structure ◽  
New Variant ◽  
Basic Characteristics ◽  
Atom Bond ◽  
Structure Descriptor

The atom-bond connectivity index (ABC) is a degree-based molecular structure descriptor with well-documented chemical applications. In 2010 a distance-based new variant of this index (ABCGG) has been proposed. Until now, the relation between ABC and ABCGG has not been analyzed. In this paper, we establish the basic characteristics of this relation. In particular, ABC and ABCGG are not correlated and both cases ABC > ABCGG and ABC < ABCGG may occur in the case of (structurally similar) molecules. However, in the case of benzenoid hydrocarbons, ABC always exceeds ABCGG.

Atom Bond Connectivity Index of Molecular Graphs of Alkynes and Cycloalkynes

2016 ◽  
Vol 13 (10) ◽  
pp. 6698-6706
Author(s):  
Mohanad A Mohammed ◽  
K. A Atan ◽  
A. M Khalaf ◽  
R Hasni ◽  
M. R. Md Said
Keyword(s):  
Molecular Structure ◽  
Connectivity Index ◽  
Molecular Graphs ◽  
Degree Of A Vertex ◽  
Abc Index ◽  
Atom Bond

The atom-bond connectivity (ABC) index is one of the recently most investigated degree based molecular structure descriptors that have applications in chemistry. For a graph G, the ABC index is defined as ABC(G) = <inline-formula> <mml:math display="block"> <mml:msub> <mml:mo>∑</mml:mo> <mml:mrow> <mml:mi>u</mml:mi><mml:mi>v</mml:mi><mml:mo>∈</mml:mo><mml:mi>E</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>G</mml:mi><mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msub> <mml:msqrt> <mml:mrow> <mml:mo stretchy="false">[</mml:mo><mml:msub> <mml:mi>d</mml:mi> <mml:mi>v</mml:mi> </mml:msub> <mml:mo>+</mml:mo><mml:msub> <mml:mi>d</mml:mi> <mml:mi>u</mml:mi> </mml:msub> <mml:mo>−</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">]</mml:mo><mml:mo>/</mml:mo><mml:mo stretchy="false">[</mml:mo><mml:msub> <mml:mi>d</mml:mi> <mml:mi>v</mml:mi> </mml:msub> <mml:mtext> </mml:mtext><mml:mo>·</mml:mo><mml:mtext> </mml:mtext><mml:msub> <mml:mi>d</mml:mi> <mml:mi>u</mml:mi> </mml:msub> <mml:mo stretchy="false">]</mml:mo><mml:mo>,</mml:mo> </mml:mrow> </mml:msqrt> </mml:math> </inline-formula> where du denotes the degree of a vertex u in G. In this paper, we establish the general formulas for the atom bond connectivity index of molecular graphs of alkynes and cycloalkynes.

scholarly journals Relating the ABC and harmonic indices

2014 ◽  
Vol 79 (5) ◽  
pp. 557-563 ◽  
Author(s):  
Ivan Gutman ◽  
Lingping Zhong ◽  
Kexiang Xu
Keyword(s):  
Molecular Structure ◽  
Topological Index ◽  
Molecular Graph ◽  
Vertex Degree ◽  
Harmonic Index ◽  
Abc Index ◽  
Atom Bond ◽  
Structure Descriptor

The atom-bond connectivity (ABC) index is a much-studied molecular structure descriptor, based on the degrees of the vertices of the molecular graph. Recently, another vertex-degree-based topological index - the harmonic index (H) - attracted attention and gained popularity. We show how ABC and H are related.

scholarly journals Relating Estrada index with spectral radius

2007 ◽  
Vol 72 (12) ◽  
pp. 1321-1327 ◽  
Author(s):  
Ivan Gutman ◽  
Slavko Radenkovic ◽  
Boris Furtula ◽  
Toufik Mansour ◽  
Matthias Schork
Keyword(s):  
Molecular Structure ◽  
Spectral Radius ◽  
Organic Molecules ◽  
Molecular Graph ◽  
3D Structure ◽  
Estrada Index ◽  
Basic Characteristics ◽  
Structure Descriptor ◽  
Long Chain

The Estrada index EE is a recently proposed molecular structure-descriptor, used in the modeling of certain features of the 3D structure of organic molecules, in particular of the degree of folding of proteins and other long-chain biopolymers. The Estrada index is computed from the spectrum of the molecular graph. Therefore, finding its relation with the spectral radius r (= the greatest graph eigenvalue) is of interest, especially because the structure-dependency of r is relatively well understood. In this work, the basic characteristics of the relation between EE and r, which turned out to be much more complicated than initially anticipated, was determined.

Extended energy and its dependence on molecular structure

2017 ◽  
Vol 95 (5) ◽  
pp. 526-529 ◽  
Author(s):  
Ivan Gutman ◽  
Boris Furtula ◽  
Kinkar Ch. Das
Keyword(s):  
Molecular Structure ◽  
Electron Energy ◽  
Topological Index ◽  
Molecular Properties ◽  
Vertex Degree ◽  
Energy Formula ◽  
The Difference ◽  
Basic Characteristics ◽  
Ga Index ◽  
Structure Descriptor

The extended energy ([Formula: see text]) is a vertex degree based and spectrum-based molecular structure descriptor, shown to be well correlated with a variety of physicochemical molecular properties. We investigate the dependence of [Formula: see text] on molecular structure and establish its basic characteristics. In particular, we show how [Formula: see text] is related with the geometric–arithmetic (GA) topological index. Our main finding is that the difference between [Formula: see text] and the total π-electron energy is linearly proportional to the difference between the number of edges and the GA index.

scholarly journals Study of Hardness of Superhard Crystals by Topological Indices

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Xiujun Zhang ◽  
Muhammad Naeem ◽  
Abdul Qudair Baig ◽  
Manzoor Ahmad Zahid
Keyword(s):  
Molecular Structure ◽  
Chemical Structure ◽  
Topological Indices ◽  
Connectivity Index ◽  
Chemical Bonds ◽  
Randić Index ◽  
Total Resistance ◽  
Randic Index ◽  
Atom Bond

Topological indices give immense information about a molecular structure or chemical structure. The hardness of materials for the indentation can be defined microscopically as the total resistance and effect of chemical bonds in the respective materials. The aim of this paper is to study the hardness of some superhard B C x crystals by means of topological indices, specifically Randić index and atom-bond connectivity index.

Eccentric Connectivity Index of Molecular Grapgs of Chemical Trees with Application to Alkynes

2016 ◽  
Vol 13 (10) ◽  
pp. 6694-6697 ◽  
Author(s):  
R. S Haoer ◽  
K. A Atan ◽  
A. M Khalaf ◽  
M. R. Md Said ◽  
R Hasni
Keyword(s):  
Molecular Structure ◽  
Mathematical Modelling ◽  
Biological Activities ◽  
Molecular Graph ◽  
Connectivity Index ◽  
Chemical Bonds ◽  
Eccentric Connectivity Index ◽  
Degree Of A Vertex ◽  
Structure Descriptor ◽  
Chemical Trees

Let G = (V,E) be a simple connected molecular graph. The eccentric connectivity index ξ(G) is a distance–based molecular structure descriptor that was recently used for mathematical modelling of biological activities of diverse nature. In such a simple molecular graph, vertices represent atoms and edges represent chemical bonds, we denoted the sets of vertices and edges by V = V(G) and E = E(G), respectively. If d(u,v) be the notation of distance between vertices u,v ∈ V and is defined as the length of a shortest path connecting them. Then, the eccentricity connectivity index of a molecular graph Gis defined as ξ(G) = Σv∈V(G) deg(V)ec(V), where deg(V) (or simply dv) is degree of a vertex V ∈ V(G), and is defined as the number of adjacent vertices with V. ec(V) is defined as the length of a maximal path connecting to another vertex of v. In this paper, we establish the general formulas for the eccentricity connectivity index of molecular graphs classes of chemical trees with application to alkynes.

On eccentricity-based topological descriptors of water-soluble dendrimers

2018 ◽  
Vol 74 (1-2) ◽  
pp. 25-33 ◽  
Author(s):  
Zahid Iqbal ◽  
Muhammad Ishaq ◽  
Adnan Aslam ◽  
Wei Gao
Keyword(s):  
Molecular Structure ◽  
Chemical Properties ◽  
Topological Indices ◽  
Water Soluble ◽  
Connectivity Index ◽  
Topological Descriptors ◽  
Physical And Chemical Properties ◽  
Eccentric Connectivity Index ◽  
Physical And Chemical ◽  
And Chemical Properties

AbstractPrevious studies show that certain physical and chemical properties of chemical compounds are closely related with their molecular structure. As a theoretical basis, it provides a new way of thinking by analyzing the molecular structure of the compounds to understand their physical and chemical properties. The molecular topological indices are numerical invariants of a molecular graph and are useful to predict their bioactivity. Among these topological indices, the eccentric-connectivity index has a prominent place, because of its high degree of predictability of pharmaceutical properties. In this article, we compute the closed formulae of eccentric-connectivity–based indices and its corresponding polynomial for water-soluble perylenediimides-cored polyglycerol dendrimers. Furthermore, the edge version of eccentric-connectivity index for a new class of dendrimers is determined. The conclusions we obtained in this article illustrate the promising application prospects in the field of bioinformatics and nanomaterial engineering.

scholarly journals Some inequalities for the atom-bond connectivity index of graph operations

2011 ◽  
Vol 159 (13) ◽  
pp. 1323-1330 ◽  
Author(s):  
G.H. Fath-Tabar ◽  
B. Vaez-Zadeh ◽  
A.R. Ashrafi ◽  
A. Graovac
Keyword(s):  
Connectivity Index ◽  
Graph Operations ◽  
Atom Bond

scholarly journals On Atom-Bond Connectivity Index

2011 ◽  
Vol 66a ◽  
pp. 61 ◽  
Author(s):  
Zhou B. ◽  
Xing R.
Keyword(s):  
Connectivity Index ◽  
Atom Bond
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