scholarly journals Edge Metric and Fault-Tolerant Edge Metric Dimension of Hollow Coronoid

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1405
Author(s):  
Ali N. A. Koam ◽  
Ali Ahmad ◽  
Muhammad Ibrahim ◽  
Muhammad Azeem
Keyword(s):  
Graph Theory ◽  
Chemical Structure ◽  
Fault Tolerant ◽  
Organic Chemical ◽  
Metric Dimension ◽  
Chemical Structures ◽  
Geometric Arrangements

Geometric arrangements of hexagons into six sides of benzenoids are known as coronoid systems. They are organic chemical structures by definition. Hollow coronoids are divided into two types: primitive and catacondensed coronoids. Polycyclic conjugated hydrocarbon is another name for them. Chemical mathematics piques the curiosity of scientists from a variety of disciplines. Graph theory has always played an important role in making chemical structures intelligible and useful. After converting a chemical structure into a graph, many theoretical and investigative studies on structures can be carried out. Among the different parameters of graph theory, the dimension of edge metric is the most recent, unique, and important parameter. Few proposed vertices are picked in this notion, such as all graph edges have unique locations or identifications. Different (edge) metric-based concept for the structure of hollow coronoid were discussed in this study.

scholarly journals Computation of Edge Resolvability of Benzenoid Tripod Structure

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Ali Ahmad ◽  
Sadia Husain ◽  
Muhammad Azeem ◽  
Kashif Elahi ◽  
M. K. Siddiqui
Keyword(s):  
Fault Tolerant ◽  
Pharmaceutical Research ◽  
Chemical Compounds ◽  
Metric Dimension ◽  
Resolving Set ◽  
Unique Representation ◽  
Chemical Structures ◽  
Distance Vector

In chemistry, graphs are commonly used to show the structure of chemical compounds, with nodes and edges representing the atom and bond types, respectively. Edge resolving set λ e is an ordered subset of nodes of a graph C , in which each edge of C is distinctively determined by its distance vector to the nodes in λ . The cardinality of a minimum edge resolving set is called the edge metric dimension of C . An edge resolving set L e , f of C is fault-tolerant if λ e , f ∖ b is also an edge resolving set, for every b in λ e , f . Resolving set allows obtaining a unique representation for chemical structures. In particular, they were used in pharmaceutical research for discovering patterns common to a variety of drugs. In this paper, we determine the exact edge metric and fault-tolerant edge metric dimension of benzenoid tripod structure and proved that both parameters are constant.

scholarly journals Fault-Tolerant Resolvability in Some Classes of Line Graphs

2020 ◽  
Vol 2020 ◽  
pp. 1-8 ◽  
Author(s):  
Xuan Guo ◽  
Muhammad Faheem ◽  
Zohaib Zahid ◽  
Waqas Nazeer ◽  
Jingjng Li
Keyword(s):  
Graph Theory ◽  
Fault Tolerance ◽  
Fault Tolerant ◽  
Stable System ◽  
Subject Classification ◽  
Metric Dimension ◽  
Line Graphs ◽  
Resolving Set ◽  
Minimum Cardinality

Fault tolerance is the characteristic of a system that permits it to carry on its intended operations in case of the failure of one of its units. Such a system is known as the fault-tolerant self-stable system. In graph theory, if we remove any vertex in a resolving set, then the resulting set is also a resolving set, called the fault-tolerant resolving set, and its minimum cardinality is called the fault-tolerant metric dimension. In this paper, we determine the fault-tolerant resolvability in line graphs. As a main result, we computed the fault-tolerant metric dimension of line graphs of necklace and prism graphs (2010 Mathematics Subject Classification: 05C78).

scholarly journals A Comparative Study of Three Resolving Parameters of Graphs

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Hafiz Muhammad Ikhlaq ◽  
Hafiz Muhammad Afzal Siddiqui ◽  
Muhammad Imran
Keyword(s):  
Image Processing ◽  
Pattern Recognition ◽  
Graph Theory ◽  
Comparative Analysis ◽  
Line Graph ◽  
Metric Dimension ◽  
Chemical Structures ◽  
Digital World ◽  
Diffusion Mechanisms ◽  
Mixed Metric

Graph theory is one of those subjects that is a vital part of the digital world. It is used to monitor the movement of robots on a network, to debug computer networks, to develop algorithms, and to analyze the structural properties of chemical structures, among other things. It is also useful in airplane scheduling and the study of diffusion mechanisms. The parameters computed in this article are very useful in pattern recognition and image processing. A number d f , w = min d w , t , d w , s is referred as distance between f = t s an edge and w a vertex. d w , f 1 ≠ d w , f 2 implies that two edges f 1 , f 2 ∈ E are resolved by node w ∈ V . A set of nodes A is referred to as an edge metric generator if every two links/edges of Γ are resolved by some nodes of A and least cardinality of such sets is termed as edge metric dimension, e dim Γ for a graph Γ . A set B of some nodes of Γ is a mixed metric generator if any two members of V ∪ E are resolved by some members of B . Such a set B with least cardinality is termed as mixed metric dimension, m dim Γ . In this paper, the metric dimension, edge metric dimension, and mixed metric dimension of dragon graph T n , m , line graph of dragon graph L T n , m , paraline graph of dragon graph L S T n , m , and line graph of line graph of dragon graph L L T n , m have been computed. It is shown that these parameters are constant, and a comparative analysis is also given for the said families of graphs.

Chemical structure of diamond-like carbon thin films

1990 ◽  
Vol 48 (4) ◽  
pp. 710-711
Author(s):  
N.-H. Cho ◽  
K.M. Krishnan ◽  
D.B. Bogy
Keyword(s):  
Electrical Resistivity ◽  
Chemical Structure ◽  
Diamond Like Carbon ◽  
Chemical Structures ◽  
Sputtering Power ◽  
Data Aquisition ◽  
Equilibrium Phases ◽  
Electron Energy Loss ◽  
Power Densities ◽  
Preparation Techniques

Diamond-like carbon (DLC) films have attracted much attention due to their useful properties and applications. These properties are quite variable depending on film preparation techniques and conditions, DLC is a metastable state formed from highly non-equilibrium phases during the condensation of ionized particles. The nature of the films is therefore strongly dependent on their particular chemical structures. In this study, electron energy loss spectroscopy (EELS) was used to investigate how the chemical bonding configurations of DLC films vary as a function of sputtering power densities. The electrical resistivity of the films was determined, and related to their chemical structure.DLC films with a thickness of about 300Å were prepared at 0.1, 1.1, 2.1, and 10.0 watts/cm2, respectively, on NaCl substrates by d.c. magnetron sputtering. EEL spectra were obtained from diamond, graphite, and the films using a JEOL 200 CX electron microscope operating at 200 kV. A Gatan parallel EEL spectrometer and a Kevex data aquisition system were used to analyze the energy distribution of transmitted electrons. The electrical resistivity of the films was measured by the four point probe method.

scholarly journals A Further Comprehensive Review on the Phytoconstituents from the Genus Erythrina

2020 ◽  
Vol 23 (1) ◽  
pp. 65-77 ◽  
Author(s):  
Mohammad Musarraf Hussain
Keyword(s):  
Chemical Structure ◽  
Biological Activities ◽  
Chemical Constituents ◽  
Pharmaceutical Journal ◽  
Significant Source ◽  
Comprehensive Review ◽  
Chemical Structures ◽  
Previous Review

Erythrina is a significant source of phytoconstituents. The aim of this review is to solicitude of classification, synthesis, and phytochemicals with biological activities of Erythrina. In our previous review on this genus (Hussain et. al., 2016a) fifteen species (Erythrina addisoniae, E. caribeae, E. indica, E. lattisima, E. melanacantha, E. mildbraedii, E. poeppigiama, E. stricta, E. subumbrans, E. veriagata, E. vespertilio, E. velutina, E. zeberi, E. zeyheri and E. americana) have been studied and 155 molecules with chemical structures were reported. A further comprehensive review was done upon continuation on the same genus and thirteen species (E. abyssinica, E. arborescens, E. berteroana, E. burttii, E. caffra, E. coralloids, E. crista-galli, E. fusca, E. herbaceae, E. lysistemon, E. mulungu, E. speciosa and E. tahitensis) of Erythrina have been studied and 127 compounds are reported as phytoconstituents with their chemical structure in this review. Erythrina crista-galli and E. lysistemon consist of highest number of chemical constituents. Bangladesh Pharmaceutical Journal 23(1): 65-77, 2020

scholarly journals A Review of Bacteriochlorophyllides: Chemical Structures and Applications

Molecules ◽  
2021 ◽  
Vol 26 (5) ◽  
pp. 1293
Author(s):  
Chih-Hui Yang ◽  
Keng-Shiang Huang ◽  
Yi-Ting Wang ◽  
Jei-Fu Shaw
Keyword(s):  
Solar Cell ◽  
Energy Harvesting ◽  
Chemical Structure ◽  
The Other ◽  
Dye Sensitized Solar Cell ◽  
Synthetic Route ◽  
Chemical Structures ◽  
Dye Sensitized ◽  
Heme Synthesis ◽  
Potential Applications

Generally, bacteriochlorophyllides were responsible for the photosynthesis in bacteria. Seven types of bacteriochlorophyllides have been disclosed. Bacteriochlorophyllides a/b/g could be synthesized from divinyl chlorophyllide a. The other bacteriochlorophyllides c/d/e/f could be synthesized from chlorophyllide a. The chemical structure and synthetic route of bacteriochlorophyllides were summarized in this review. Furthermore, the potential applications of bacteriochlorophyllides in photosensitizers, immunosensors, influence on bacteriochlorophyll aggregation, dye-sensitized solar cell, heme synthesis and for light energy harvesting simulation were discussed.

scholarly journals Uncertainty-Informed Deep Transfer Learning of PFAS Toxicity

2021 ◽  
Author(s):  
Jeremy Feinstein ◽  
ganesh sivaraman ◽  
Kurt Picel ◽  
Brian Peters ◽  
Alvaro Vazquez-Mayagoitia ◽  
...  
Keyword(s):  
Machine Learning ◽  
Transfer Learning ◽  
High Throughput ◽  
High Throughput Screening ◽  
Organic Chemical ◽  
Learning Method ◽  
Toxicity Data ◽  
Chemical Structures ◽  
Machine Learning Methods ◽  
Computational Methodology

In this article, we present our recent study on computational methodology for predicting the toxicity of PFAS known as “forever chemicals” based on chemical structures through evaluation of multiple machine learning methods. To address the scarcity of PFAS toxicity data, a deep “transfer learning” method has been investigated by leveraging toxicity information over the entire organic chemical domain and an uncertainty-informed workflow by incorporating SelectiveNet architecture, which can support future guidance of high throughput screening with knowledge of chemical structures, has been developed.

scholarly journals Metric Dimension in fuzzy(neutrosophic) Graphs-VII

2021 ◽  
Author(s):  
Henry Garrett
Keyword(s):  
Graph Theory ◽  
Individual Case ◽  
Metric Dimension ◽  
Neutrosophic Graph ◽  
Distinct Distance ◽  
Optimal Set ◽  
Dimension Number

New notion of dimension as set, as two optimal numbers including metric number, dimension number and as optimal set are introduced in individual framework and in formation of family. Behaviors of twin and antipodal are explored in fuzzy(neutrosophic) graphs. Fuzzy(neutrosophic) graphs, under conditions, fixed-edges, fixed-vertex and strong fixed-vertex are studied. Some classes as path, cycle, complete, strong, t-partite, bipartite, star and wheel in the formation of individual case and in the case, they form a family are studied in the term of dimension. Fuzzification(neutrosofication) of twin vertices but using crisp concept of antipodal vertices are another approaches of this study. Thus defining two notions concerning vertices which one of them is fuzzy(neutrosophic) titled twin and another is crisp titled antipodal to study the behaviors of cycles which are partitioned into even and odd, are concluded. Classes of cycles according to antipodal vertices are divided into two classes as even and odd. Parity of the number of edges in cycle causes to have two subsections under the section is entitled to antipodal vertices. In this study, the term dimension is introduced on fuzzy(neutrosophic) graphs. The locations of objects by a set of some junctions which have distinct distance from any couple of objects out of the set, are determined. Thus it’s possible to have the locations of objects outside of this set by assigning partial number to any objects. The classes of these specific graphs are chosen to obtain some results based on dimension. The types of crisp notions and fuzzy(neutrosophic) notions are used to make sense about the material of this study and the outline of this study uses some new notions which are crisp and fuzzy(neutrosophic). Some questions and problems are posed concerning ways to do further studies on this topic. Basic familiarities with fuzzy(neutrosophic) graph theory and graph theory are proposed for this article.

scholarly journals Dimensi Metrik Kuat Lokal Graf Hasil Operasi Kali Kartesian

2020 ◽  
Vol 1 (2) ◽  
pp. 64
Author(s):  
Nurma Ariska Sutardji ◽  
Liliek Susilowati ◽  
Utami Dyah Purwati
Keyword(s):  
Graph Theory ◽  
Cartesian Product ◽  
Metric Dimension ◽  
Star Graph ◽  
Product Graph ◽  
Path Graph ◽  
Strong Metric Dimension ◽  
Metric Dimensions ◽  
Development Result ◽  
Corona Product

The strong local metric dimension is the development result of a strong metric dimension study, one of the study topics in graph theory. Some of graphs that have been discovered about strong local metric dimension are path graph, star graph, complete graph, cycle graphs, and the result corona product graph. In the previous study have been built about strong local metric dimensions of corona product graph. The purpose of this research is to determine the strong local metric dimension of cartesian product graph between any connected graph G and H, denoted by dimsl (G x H). In this research, local metric dimension of G x H is influenced by local strong metric dimension of graph G and local strong metric dimension of graph H. Graph G and graph H has at least two order.

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