On vertex PI index of certain triangular tessellation networks

2021 ◽  
Vol 44 (1) ◽  
pp. 203-212
Author(s):  
Syed Ahtsham Ul Haq Bokhary ◽  
Adnan
Keyword(s):  
Biological Activities ◽  
Molecular Graph ◽  
Chemical Compounds ◽  
Wiener Index ◽  
Theoretic Analysis ◽  
Complex Chemical ◽  
Chemical Graph ◽  
Graph Theoretic ◽  
Pi Index ◽  
Triangular Tessellation

Abstract The Wiener index, due to its many applications is considered to be one of very important distance-based index. But the Padmaker-Ivan (PI) index is kind of the only distance related index linked to parallelism of edges. The PI index like other distance related indices has great disseminating power. The index was firstly investigated by Khadikar et al. (2001), they have probed the chemical applications of the PI index. They proved that the proposed PI index correlates highly with the physicochemical properties and biological activities of a large number of diverse and complex chemical compounds and the Wiener and Szeged indices. Recently, the vertex Padmarkar-Ivan (PIv) index of a chemical graph G was introduced as the sum over all edges uv of a molecular graph G of the vertices of the graph that are not equidistant to the vertices u and v. In this paper, the vertex PIv index of certain triangular tessellation are computed by using graph-theoretic analysis, combinatorial computing, and edge-dividing technology.

scholarly journals On Wiener Polarity Index and Wiener Index of Certain Triangular Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Mr. Adnan ◽  
Syed Ahtsham Ul Haq Bokhary ◽  
Muhammad Imran
Keyword(s):  
Chemical Compounds ◽  
Wiener Index ◽  
Topological Indices ◽  
Index Number ◽  
Graph Theoretic ◽  
Polarity Index ◽  
Boiling Points ◽  
Van Der Waals Surface ◽  
Density Surface ◽  
Quantitative Structure Activity Relationships

A topological index of graph G is a numerical quantity which describes its topology. If it is applied to the molecular structure of chemical compounds, it reflects the theoretical properties of the chemical compounds. A number of topological indices have been introduced so far by different researchers. The Wiener index is one of the oldest molecular topological indices defined by Wiener. The Wiener index number reflects the index boiling points of alkane molecules. Quantitative structure activity relationships (QSAR) showed that they also describe other quantities including the parameters of its critical point, density, surface tension, viscosity of its liquid phase, and the van der Waals surface area of the molecule. The Wiener polarity index has been introduced by Wiener and known to be related to the cluster coefficient of networks. In this paper, the Wiener polarity index W p G and Wiener index W G of certain triangular networks are computed by using graph-theoretic analysis, combinatorial computing, and vertex-dividing technology.

scholarly journals On Some Properties of Multiplicative Topological Indices in Silicon-Carbon

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Abid Mahboob ◽  
Sajid Mahboob ◽  
Mohammed M. M. Jaradat ◽  
Nigait Nigar ◽  
Imran Siddique
Keyword(s):  
Graph Theory ◽  
Structural Properties ◽  
Topological Index ◽  
Molecular Graph ◽  
Chemical Compounds ◽  
Google Maps ◽  
Chemical Graph ◽  
Zagreb Indices ◽  
Silicon Carbon ◽  
Connectivity Indices

The use of graph theory can be visualized in nanochemistry, computer networks, Google maps, and molecular graph which are common areas to elaborate application of this subject. In nanochemistry, a numeric number (topological index) is used to estimate the biological, physical, and structural properties of chemical compounds that are associated with the chemical graph. In this paper, we compute the first and second multiplicative Zagreb indices ( M 1 G and ( M 1 G )), generalized multiplicative geometric arithmetic index ( GA α II G ), and multiplicative sum connectivity and multiplicative product connectivity indices ( SCII G and PCII G ) of SiC 4 − I m , n and SiC 4 − II m , n .

Analysis of Bioactive Chemical Compounds of Trogoderma granarium (Insecta: Coleoptera: Dermestidae) Using Gas Chromatography – Mass Spectrometry

2017 ◽  
Vol 9 (03) ◽  
Author(s):  
Jenan Mohammed Ubaid ◽  
Abeer Fauzi Al-Rubaye ◽  
Imad Hadi Hameed
Keyword(s):  
Acetic Acid ◽  
Benzoyl Chloride ◽  
Methanolic Extract ◽  
Biological Activities ◽  
Chemical Compounds ◽  
Gas Chromatography Mass Spectrometry ◽  
Pentanoic Acid ◽  
Trogoderma Granarium ◽  
Trans Methyl ◽  
Phenacyl Thiocyanate

Methanolic extract of bioactive compounds of Trogoderma granarium was assayed. GC-MS analysis of Trogoderma granarium revealed the existence of the Pentanoic acid , 1,1-dimethylpropyl ester , (1H)-Pyrimidinone , 5-chloro-4,6- diphenyl, Cyclobutanemethanol , α-methyl- , Nitro-2-methyl-1,3-propanediol , Hydroxylamine ,O-(2-methylpropyl)- , Uridine , 2',3'-O-(phenylmethylene)- ,Acetic acid ,2-benzoylthio-,2-oxo-2-phenylethyl ester , methylpropyl)- , Uridine , 2',3'-O-(phenylmethylene)- , 5'-(4-methylbenzenesulfo , Indolinol , 1-benzoyl-, Benzeneethanol , β-methyl-,(s)- , Acetic acid ,2-benzoylthio-,2-oxo-2-phenylethyl ester , Phenacyl thiocyanate , Deoxy-L-ribose-2,5-dibenzoate , Methenamine , Alanine , N-methyl-n-propargyloxycarbonyl-, decyl ester , Benzoyl chloride , Thiophene-2-ol , benzoate , Ethanone , -(5- nitrotetrazol-2-yl)-1-phenyl- , 2,5-Dimethylhexane-2,5-dihydroperoxide , Benzamide , N-(3-benzylthio-1,2,4-thiadiazol- 5-yl)- , Methyl p-(2-phenyl-1-benzimidazolyl)benzoate , Methyl-2-phenoxyethylamine , Pentaborane(11) , cis-Methoxy- 5-trans-methyl-1R-cyclohexanol , Nitro-1-phenyl-3-(tetrahydropyran-2-yloxy)propan-1-one , cis-Methoxy-5-transmethyl-1R-cyclohexanol. Trogoderma granarium produce many important secondary metabolites with high biological activities.

Secondary Metabolites of Plant Origin containing Carbazole as Lead Molecule: A Review

2019 ◽  
Vol 05 ◽  
Author(s):  
Atul Sharma ◽  
Devender Pathak
Keyword(s):  
Drug Discovery ◽  
Heterocyclic Compounds ◽  
Biological Activities ◽  
Chemical Compounds ◽  
Lethal Effect ◽  
Chemical Diversity ◽  
Chemical Transformations ◽  
Pharmacological Effects ◽  
Structural Class ◽  
Biological Targets

Keeping this fact that study of a body is biology but life is all about chemicals and chemical transformations, many medicinal chemist start research in finding new and novel chemical compounds which having pharmacological activities. Most of those chemical compounds which are having active pharmacological effects are heterocyclic compounds. Heterocyclic compounds clutch a particular place among pharmaceutically active natural and synthetic compounds. The ability to serve both as biomimetics and reactive pharmacophores of heterocyclic nuclei is incredible and it has principally contributed to their unique value as traditional key elements of numerous drugs. These heterocyclic nuclei offer a huge area for new lead molecules for drug discovery and for generation of activity relationships with biological targets to enhance pharmacological effects. For these reasons, it is not surprising that this structural class has received special attention in drug discovery. The hydrogen bond acceptors and donors arranged in a manner of a semi-rigid skeleton in heterocyclic rings and therefore they can present a varied display of significant pharmacophores. Lead identification and optimization of drug target probable can be achieved by generation of chemical diversity produced by derivatization of heterocyclic pharmacophores with different groups or substituents. A tricyclic carbazole nucleus is an integral part of naturally occurring alkaloids and synthetic derivatives, possessing various potential biological activities such as anticancer, antimicrobial and antiviral. Binding mechanism of carbazole with target receptor as a molecule or fused molecule exhibits the potential lethal effect.

scholarly journals Computing Topological Indices for Para-Line Graphs of Anthracene

2019 ◽  
Vol 17 (1) ◽  
pp. 955-962 ◽  
Author(s):  
Zhiqiang Zhang ◽  
Zeshan Saleem Mufti ◽  
Muhammad Faisal Nadeem ◽  
Zaheer Ahmad ◽  
Muhammad Kamran Siddiqui ◽  
...  
Keyword(s):  
Graph Theory ◽  
Chemical Compound ◽  
Line Graph ◽  
Molecular Graph ◽  
Chemical Properties ◽  
Molar Refraction ◽  
Chromatographic Behavior ◽  
Chemical Graph ◽  
Chemical Graph Theory ◽  
And Mathematics

AbstractAtoms displayed as vertices and bonds can be shown by edges on a molecular graph. For such graphs we can find the indices showing their bioactivity as well as their physio-chemical properties such as the molar refraction, molar volume, chromatographic behavior, heat of atomization, heat of vaporization, magnetic susceptibility, and the partition coefficient. Today, industry is flourishing because of the interdisciplinary study of different disciplines. This provides a way to understand the application of different disciplines. Chemical graph theory is a mixture of chemistry and mathematics, which plays an important role in chemical graph theory. Chemistry provides a chemical compound, and graph theory transforms this chemical compound into a molecular graphwhich further is studied by different aspects such as topological indices.We will investigate some indices of the line graph of the subdivided graph (para-line graph) of linear-[s] Anthracene and multiple Anthracene.

scholarly journals On multiplicative degree based topological indices for planar octahedron networks

2020 ◽  
Vol 43 (1) ◽  
pp. 219-228
Author(s):  
Ghulam Dustigeer ◽  
Haidar Ali ◽  
Muhammad Imran Khan ◽  
Yu-Ming Chu
Keyword(s):  
Graph Theory ◽  
Information Science ◽  
Biological Activities ◽  
Molecular Graph ◽  
Triangular Prism ◽  
Structure Property ◽  
Zagreb Index ◽  
Zagreb Indices ◽  
Chemical Graph Theory ◽  
Analytical Formulas

AbstractChemical graph theory is a branch of graph theory in which a chemical compound is presented with a simple graph called a molecular graph. There are atomic bonds in the chemistry of the chemical atomic graph and edges. The graph is connected when there is at least one connection between its vertices. The number that describes the topology of the graph is called the topological index. Cheminformatics is a new subject which is a combination of chemistry, mathematics and information science. It studies quantitative structure-activity (QSAR) and structure-property (QSPR) relationships that are used to predict the biological activities and properties of chemical compounds. We evaluated the second multiplicative Zagreb index, first and second universal Zagreb indices, first and second hyper Zagreb indices, sum and product connectivity indices for the planar octahedron network, triangular prism network, hex planar octahedron network, and give these indices closed analytical formulas.

Graph-Theoretic Analysis of Power Grid Robustness

2021 ◽  
pp. 175-194
Author(s):  
Dorcas Ofori-Boateng ◽  
Asim Kumer Dey ◽  
R. Gel Yulia ◽  
H. Vincent Poor
Keyword(s):  
Power Grid ◽  
Theoretic Analysis ◽  
Graph Theoretic

Bounds on hyper-Wiener index of graphs

2017 ◽  
Vol 10 (03) ◽  
pp. 1750057
Author(s):  
Abdollah Alhevaz ◽  
Maryam Baghipur ◽  
Sadegh Rahimi
Keyword(s):  
Lower Bounds ◽  
Organic Molecules ◽  
Wiener Index ◽  
Upper And Lower Bounds ◽  
Pharmacological Properties ◽  
Graph Theoretic ◽  
Acyclic Graphs ◽  
Wiener Number ◽  
Number Formula ◽  
Cyclic Graphs

The Wiener number [Formula: see text] of a graph [Formula: see text] was introduced by Harold Wiener in connection with the modeling of various physic-chemical, biological and pharmacological properties of organic molecules in chemistry. Milan Randić introduced a modification of the Wiener index for trees (acyclic graphs), and it is known as the hyper-Wiener index. Then Klein et al. generalized Randić’s definition for all connected (cyclic) graphs, as a generalization of the Wiener index, denoted by [Formula: see text] and defined as [Formula: see text]. In this paper, we establish some upper and lower bounds for [Formula: see text], in terms of other graph-theoretic parameters. Moreover, we compute hyper-Wiener number of some classes of graphs.

scholarly journals Integrative statistical analyses of multiple liquid biopsy analytes in metastatic breast cancer

2021 ◽  
Vol 13 (1) ◽  
Author(s):  
Corinna Keup ◽  
Vinay Suryaprakash ◽  
Siegfried Hauch ◽  
Markus Storbeck ◽  
Peter Hahn ◽  
...  
Keyword(s):  
Breast Cancer ◽  
Overall Survival ◽  
Metastatic Breast Cancer ◽  
Mutual Information ◽  
Hierarchical Clustering ◽  
Liquid Biopsy ◽  
Metastatic Breast ◽  
The Other ◽  
Theoretic Analysis ◽  
Graph Theoretic

Abstract Background Single liquid biopsy analytes (LBAs) have been utilized for therapy selection in metastatic breast cancer (MBC). We performed integrative statistical analyses to examine the clinical relevance of using multiple LBAs: matched circulating tumor cell (CTC) mRNA, CTC genomic DNA (gDNA), extracellular vesicle (EV) mRNA, and cell-free DNA (cfDNA). Methods Blood was drawn from 26 hormone receptor-positive, HER2-negative MBC patients. CTC mRNA and EV mRNA were analyzed using a multi-marker qPCR. Plasma from CTC-depleted blood was utilized for cfDNA isolation. gDNA from CTCs was isolated from mRNA-depleted CTC lysates. CTC gDNA and cfDNA were analyzed by targeted sequencing. Hierarchical clustering was performed within each analyte, and its results were combined into a score termed Evaluation of multiple Liquid biopsy analytes In Metastatic breast cancer patients All from one blood sample (ELIMA.score), which calculates the contribution of each analyte to the overall survival prediction. Singular value decomposition (SVD), mutual information calculation, k-means clustering, and graph-theoretic analysis were conducted to elucidate the dependence between individual analytes. Results A combination of two/three/four LBAs increased the prevalence of patients with actionable signals. Aggregating the results of hierarchical clustering of individual LBAs into the ELIMA.score resulted in a highly significant correlation with overall survival, thereby bolstering evidence for the additive value of using multiple LBAs. Computation of mutual information indicated that none of the LBAs is independent of the others, but the ability of a single LBA to describe the others is rather limited—only CTC gDNA could partially describe the other three LBAs. SVD revealed that the strongest singular vectors originate from all four LBAs, but a majority originated from CTC gDNA. After k-means clustering of patients based on parameters of all four LBAs, the graph-theoretic analysis revealed CTC ERBB2 variants only in patients belonging to one particular cluster. Conclusions The additional benefits of using all four LBAs were objectively demonstrated in this pilot study, which also indicated a relative dominance of CTC gDNA over the other LBAs. Consequently, a multi-parametric liquid biopsy approach deconvolutes the genomic and transcriptomic complexity and should be considered in clinical practice.

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