Eccentric Connectivity Index:  A Novel Highly Discriminating Topological Descriptor for Structure−Property and Structure−Activity Studies

Let G be a simple graph with vertex set V(G) and edge set E(G). For ∀νi∈V(G),di denotes the degree of νi in G. The Randić connectivity index of the graph G is defined as [1-3] χ(G)=∑e=v1v2є(G)(d1d2)-1/2. The sum-connectivity index is defined as χ(G)=∑e=v1v2є(G)(d1+d2)-1/2. The sum-connectivity index is a new variant of the famous Randić connectivity index usable in quantitative structure-property relationship and quantitative structure-activity relationship studies. The general m-connectivety and general m-sum connectivity indices of G are defined as mχ(G)=∑e=v1v2...vim+1(1/√(di1di2...dim+1)) and mχ(G)=∑e=v1v2...vim+1(1/√(di1+di2+...+dim+1)) where vi1vi2...vim+1 runs over all paths of length m in G. In this paper, we introduce a closed formula of the third-connectivity index and third-sum-connectivity index of nanostructure "Armchair Polyhex Nanotubes TUAC6[m,n]" (m,n≥1).

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The eccentric version of atom-bond connectivity index of tetra sheet networks

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830918500659 ◽

2018 ◽

Vol 10 (05) ◽

pp. 1850065 ◽

Cited By ~ 1

Author(s):

Muhammad Imran ◽

Abdul Qudair Baig ◽

Muhammad Razwan Azhar

Keyword(s):

Connected Graph ◽

Molecular Graph ◽

Theoretical Chemistry ◽

Connectivity Index ◽

Maximum Distance ◽

Eccentric Connectivity Index ◽

Topological Descriptor ◽

Degree Of A Vertex ◽

Connectivity Indices ◽

Atom Bond

Among topological descriptor of graphs, the connectivity indices are very important and they have a prominent role in theoretical chemistry. The atom-bond connectivity index of a connected graph [Formula: see text] is represented as [Formula: see text], where [Formula: see text] represents the degree of a vertex [Formula: see text] of [Formula: see text] and the eccentric connectivity index of the molecular graph [Formula: see text] is represented as [Formula: see text], where [Formula: see text] is the maximum distance between the vertex [Formula: see text] and any other vertex [Formula: see text] of the graph [Formula: see text]. The new eccentric atom-bond connectivity index of any connected graph [Formula: see text] is defined as [Formula: see text]. In this paper, we compute the new eccentric atom-bond connectivity index for infinite families of tetra sheets equilateral triangular and rectangular networks.

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TOPOLOGICAL MODEL FOR THE PREDICTION OF ALPHA-1 ADRENOCEPTOR ANTAGONISTIC ACTIVITY OF ARYLPIPERAZINES

Journal of Theoretical and Computational Chemistry ◽

10.1142/s0219633604001021 ◽

2004 ◽

Vol 03 (02) ◽

pp. 245-255 ◽

Cited By ~ 3

Author(s):

VIPIN KUMAR ◽

A. K. MADAN

Keyword(s):

Antagonistic Activity ◽

Connectivity Index ◽

Eccentric Connectivity Index ◽

Data Set ◽

Wiener’S Index ◽

Topological Descriptor ◽

Group Parameter ◽

Accuracy Of Prediction ◽

The Relationship ◽

Zagreb Group Parameter

The relationship between Wiener's index — a distance-based topological descriptor, Zagreb group parameter — M 1, an adjacency-based topological descriptor, and eccentric connectivity index — an adjacency-cum-distance based topological descriptor, with the alpha-1 adrenoceptor antagonistic activity of arylpiperazines has been investigated. A training set, comprising 30 analogues, of substituted arylpiperazines was selected for the present investigations. The values of the Wiener's index, Zagreb group parameter and eccentric connectivity index and each of 30 analogues comprising the data set were computed. Resulting data was analyzed and suitable models developed after identification of active range. Subsequently, a biological activity was assigned to each analogue involved in the data set using these models, which was then compared with the reported adrenoceptor antagonistic activity. High accuracy of prediction ranging from 90–93% was observed using these models.

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A Review on Camptothecin Analogs with Promising Cytotoxic Profile

Anti-Cancer Agents in Medicinal Chemistry ◽

10.2174/1871520618666180327140956 ◽

2019 ◽

Vol 18 (13) ◽

pp. 1796-1814 ◽

Cited By ~ 3

Author(s):

Sk. Abdul Amin ◽

Nilanjan Adhikari ◽

Tarun Jha ◽

Shovanlal Gayen

Keyword(s):

Cell Lines ◽

Cancer Cell ◽

Cancer Cell Lines ◽

Structure Property ◽

Cytotoxic Potential ◽

Structure Property Relationships ◽

Structure Activity ◽

Camptothecin Analogs ◽

Pharmacokinetic Properties ◽

Quantitative Structure Activity Relationships

Camptothecin (CPT), obtained from Camptotheca acuminata (Nyssaceae), is a quinoline type of alkaloid. Apart from various traditional uses, it is mainly used as a potential cytotoxic agent acting against a variety of cancer cell lines. Though searches have been continued for last six decades, still it is a demanding task to design potent and cytotoxic CPTs. Different CPT analogs are synthesized to enhance the cytotoxic potential as well as to increase the pharmacokinetic properties of these analogs. Some of these analogs were proven to be clinically effective in different cancer cell lines. In this article, different CPT analogs have been highlighted extensively to get a detail insight about the structure-property relationships as well as different quantitative structure-activity relationships (QSARs) modeling of these analogs are also discussed. This study may be beneficial for designing newer CPT analogs in future.

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On detour index of cycloparaphenylene and polyphenylene molecular structures

Scientific Reports ◽

10.1038/s41598-021-94765-6 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

S. Prabhu ◽

Y. Sherlin Nisha ◽

M. Arulperumjothi ◽

D. Sagaya Rani Jeba ◽

V. Manimozhi

Keyword(s):

Atomic System ◽

Molecular Structures ◽

Topological Descriptors ◽

Covalent Bonds ◽

Atomic Structures ◽

Topological Descriptor ◽

Structure Activity ◽

Mathematical Correlation ◽

Benzene Rings ◽

Unique Method

AbstractCycloparaphenylene is a particle that comprises a few benzene rings associated with covalent bonds in the para positions to frame a ring-like structure. Similarly, poly (para-phenylenes) are macromolecules that include benzenoid compounds straightforwardly joined to each other by C–C bonds. Because of their remarkable architectural highlights, these structures have fascinated attention from numerous vantage focuses. Descriptors are among the most fundamental segments of prescient quantitative structure-activity and property relationship (QSAR/QSPR) demonstrating examination. They encode chemical data of particles as quantitative numbers, which are utilized to create a mathematical correlation. The nature of a predictive model relies upon great demonstrating insights, yet additionally on the extraction of compound highlights. To a great extent, Molecular topology has exhibited its adequacy in portraying sub-atomic structures and anticipating their properties. It follows a two-dimensional methodology, just thinking about the interior plan, including molecules. Explicit subsets speak the design of every atom of topological descriptors. When all around picked, these descriptors give a unique method of describing an atomic system that can represent the most significant highlights of the molecular structure. Detour index is one such topological descriptor with much application in chemistry, especially in QSAR/QSPR studies. This article presents an exact analytical expression for the detour index of cycloparaphenylene and poly (para-phenylene).

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On eccentricity-based topological descriptors of water-soluble dendrimers

Zeitschrift für Naturforschung C ◽

10.1515/znc-2018-0123 ◽

2018 ◽

Vol 74 (1-2) ◽

pp. 25-33 ◽

Cited By ~ 11

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.

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