scholarly journals Boundedness of Convex Polytopes Networks via Local Fractional Metric Dimension

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Muhammad Javaid ◽  
Hassan Zafar ◽  
Amer Aljaedi ◽  
Abdulaziz Mohammad Alanazi

Metric dimension is one of the distance-based parameter which is frequently used to study the structural and chemical properties of the different networks in the various fields of computer science and chemistry such as image processing, pattern recognition, navigation, integer programming, optimal transportation models, and drugs discovery. In particular, it is used to find the locations of robots with respect to shortest distance among the destinations, minimum consumption of time, and lesser number of the utilized nodes and to characterize the chemical compounds having unique presentation in molecular networks. The fractional metric dimension being a latest developed weighted version of the metric dimension is used in the distance-related problems of the aforementioned fields to find their nonintegral optimal solutions. In this paper, we have formulated the local resolving neighborhoods with their cardinalities for all the edges of the convex polytopes networks to compute their local fractional metric dimensions in the form of exact values and sharp bounds. Moreover, the boundedness of all the obtained results is also proved.

2021 ◽  
Vol 5 (4) ◽  
pp. 276
Author(s):  
Muhammad Javaid ◽  
Muhammad Kamran Aslam ◽  
Muhammad Imran Asjad ◽  
Bander N. Almutairi ◽  
Mustafa Inc ◽  
...  

The distance centric parameter in the theory of networks called by metric dimension plays a vital role in encountering the distance-related problems for the monitoring of the large-scale networks in the various fields of chemistry and computer science such as navigation, image processing, pattern recognition, integer programming, optimal transportation models and drugs discovery. In particular, it is used to find the locations of robots with respect to shortest distance among the destinations, minimum consumption of time, lesser number of the utilized nodes, and to characterize the chemical compounds, having unique presentations in molecular networks. After the arrival of its weighted version, known as fractional metric dimension, the rectification of distance-related problems in the aforementioned fields has revived to a great extent. In this article, we compute fractional as well as local fractional metric dimensions of web-related networks called by subdivided QCL, 2-faced web, 3-faced web, and antiprism web networks. Moreover, we analyse their final results using 2D and 3D plots.


Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1383
Author(s):  
Ali H. Alkhaldi ◽  
Muhammad Kamran Aslam ◽  
Muhammad Javaid ◽  
Abdulaziz Mohammed Alanazi

Metric dimension of networks is a distance based parameter that is used to rectify the distance related problems in robotics, navigation and chemical strata. The fractional metric dimension is the latest developed weighted version of metric dimension and a generalization of the concept of local fractional metric dimension. Computing the fractional metric dimension for all the connected networks is an NP-hard problem. In this note, we find the sharp bounds of the fractional metric dimensions of all the connected networks under certain conditions. Moreover, we have calculated the fractional metric dimension of grid-like networks, called triangular and polaroid grids, with the aid of the aforementioned criteria. Moreover, we analyse the bounded and unboundedness of the fractional metric dimensions of the aforesaid networks with the help of 2D as well as 3D plots.


Author(s):  
Nemah Sahib Mohammed Husien ◽  
Rajaa Abd Alameer Gafel ◽  
Noor Dia Jaffer

This  literature  involved  explanation  about  separation organic  components  in  mixture such  as(chromatography ,extraction ,filtration, centrifuge…) , principles of separation  , methods of separation ,types of separation , purification  of separated  compounds , conditions of separation , physical and chemical properties of  mixture.


2020 ◽  
Vol 17 (4) ◽  
pp. 89-95
Author(s):  
Alexander L. Urakov

The literature review shows that standards for the treatment of purulent diseases to date include antiseptic and disinfectants, but do not include agents that dilute and/or dissolve thick pus. It is shown that the pharmacodynamics of antiseptic and disinfectants consists in the local disinfecting effect of these agents. With local interaction with the surface of living and non-living tissues, these agents are able to sterilize it. It was found that for disinfection of the selected surfaces, these agents are used in solutions that contain these agents in concentrations that provide a denaturing effect. It is shown that denaturing action of antiseptic and disinfectants is a special case of dependence of local action of solutions of all medicines and chemical compounds on their concentration. The fact is that increasing the concentration of chemical compounds in solutions sooner or later turns that solutions into a liquid medium that is not compatible with life. Therefore, this liquid kills all cells of the micro-and macroworld. That is why the use of solutions with denaturing action provides a detrimental effect on the cells of all microorganisms and cells of the macroorganism. With local interaction with the tissues of the macroorganism, the drugs cause the following pharmacological effects: local sterilizing, irritating (local inflammatory) and cauterizing (necrotic) action. Thus solutions with denaturing concentration of one means increase the hardness, other means do not change the hardness, and the third means decrease the hardness of biological tissues, including purulent masses. From this it is concluded that today in the treatment of purulent diseases are used means, detrimental effect on all forms of life, and not means, unidirectionally acting on purulent masses. At the same time, it is shown that some of the modern antiseptic and disinfectants can change the properties of purulent masses in the right direction and optimize their removal by diluting and dissolving the thick pus. It is established that the leaders in the solvent action on thick and sticky pus are sodium bicarbonate solutions in combination with hydrogen peroxide. It is shown that solutions that effectively dissolve thick pus have special physical and chemical properties: all of them have moderate alkaline, temperature, boiling and osmotic activity. Preparations that most effectively dissolve thick pus and most quickly and completely remove it out of the purulent cavities, additionally contain carbon dioxide gas or oxygen gas under excessive pressure. In chronological order are recipes invented hygiene products with special physical and chemical properties, providing them with the ability to quickly and effectively liquefy, dissolve and remove the thick pus out of the purulent cavities. It is shown that a new group of hygiene products was discovered in Russia and was called Solvents of pus. The most effective and safe solvents of pus are warm (heated to a temperature of 42 C) solutions containing 24% sodium bicarbonate and 0.53% hydrogen peroxide.


2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Hassan Zafar ◽  
Muhammad Javaid ◽  
Ebenezer Bonyah

The parameter of distance in the theory of networks plays a key role to study the different structural properties of the understudy networks or graphs such as symmetry, assortative, connectivity, and clustering. For the purpose, with the help of the parameter of distance, various types of metric dimensions have been defined to find the locations of machines (or robots) with respect to the minimum consumption of time, the shortest distance among the destinations, and the lesser number of utilized nodes as places of the objects. In this article, the latest derived form of metric dimension called as LF-metric dimension is studied, and various results for the generalized gear networks are obtained in the form of exact values and sharp bounds under certain conditions. The LF-metric dimension of some particular cases of generalized gear networks (called as generalized wheel networks) is also illustrated. Moreover, the bounded and unboundedness of the LF-metric dimension for all obtained results is also presented.


Author(s):  
Abaid ur Rehman Virk

A topological index is a quantity expressed as a number that help us to catch symmetry of chemical compounds. With the help of quantitative structure property relationship (QSPR), we can guess physical and chemical properties of several chemical compounds. Here, we will compute Shingali & Kanabour, Gourava and hype Gourava indices for the chemical compound Nicotine.


2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Muhammad Javaid ◽  
Muhammad Kamran Aslam ◽  
Jia-Bao Liu

Distance-based numeric parameters play a pivotal role in studying the structural aspects of networks which include connectivity, accessibility, centrality, clustering modularity, complexity, vulnerability, and robustness. Several tools like these also help to resolve the issues faced by the different branches of computer science and chemistry, namely, navigation, image processing, biometry, drug discovery, and similarities in chemical compounds. For this purpose, in this article, we are considering a family of networks that exhibits rotationally symmetric behaviour known as circular ladders consisting of triangular, quadrangular, and pentagonal faced ladders. We evaluate their upper bounds of fractional metric dimensions of the aforementioned networks.


2021 ◽  
Vol 2021 ◽  
pp. 1-24
Author(s):  
Shahbaz Ali ◽  
Muhammad Khalid Mahmood ◽  
Fairouz Tchier ◽  
F. M. O. Tawfiq

The term metric or distance of a graph plays a vital role in the study to check the structural properties of the networks such as complexity, modularity, centrality, accessibility, connectivity, robustness, clustering, and vulnerability. In particular, various metrics or distance-based dimensions of different kinds of networks are used to resolve the problems in different strata such as in security to find a suitable place for fixing sensors for security purposes. In the field of computer science, metric dimensions are most useful in aspects such as image processing, navigation, pattern recognition, and integer programming problem. Also, metric dimensions play a vital role in the field of chemical engineering, for example, the problem of drug discovery and the formation of different chemical compounds are resolved by means of some suitable metric dimension algorithm. In this paper, we take rotationally symmetric and hexagonal planar networks with all possible faces. We find the sequences of the local fractional metric dimensions of proposed rotationally symmetric and planar networks. Also, we discuss the boundedness of sequences of local fractional metric dimensions. Moreover, we summarize the sequences of local fractional metric dimension by means of their graphs.


2020 ◽  
Vol 8 ◽  
Author(s):  
Yuhong Huo ◽  
Haidar Ali ◽  
Muhammad Ahsan Binyamin ◽  
Syed Sheraz Asghar ◽  
Usman Babar ◽  
...  

In theoretical chemistry, the numerical parameters that are used to characterize the molecular topology of graphs are called topological indices. Several physical and chemical properties like boiling point, entropy, heat formation, and vaporization enthalpy of chemical compounds can be determined through these topological indices. Graph theory has a considerable use in evaluating the relation of various topological indices of some derived graphs. In this article, we will compute the topological indices like Randić, first Zagreb, harmonic, augmented Zagreb, atom-bond connectivity, and geometric-arithmetic indices for chain hex-derived network of type 3 CHDN3(m,n) for different cases of m and n. We will also compute the numerical computation and graphical view to justify our results.Mathematics Subject Classification: 05C12, 05C90


Author(s):  
Shin Min Kang ◽  
Mobeen Munir ◽  
Abdul Rauf Nizami ◽  
Shazia Rafique ◽  
Waqas Nazeer

Titania is one of the most comprehensively studied nanostructures due to its widespread applications in production of catalytic, gas- sensing and corrosion- resistance materials [1]. M-polynomial of nanotubes has been vastly investigated as it produces many degree-based topological indices which are numerical parameters capturing structural and chemical properties. These indices are used in the development of quantitative structure-activity relationships (QSARs) in which the biological activity and other properties of molecules are correlated with their structure like boiling point, stability, strain energy etc of chemical compounds. In this paper, we determine M-polynomials of single-walled titanium (SW TiO2) nanotubes and recover important topological degree based indices of them to theoretically judge these nanotubes. We also use Maple to plot surfaces associated to different types of single-walled titanium (SW TiO2) nanotubes.


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