Structural Analysis of Nanoscale Network Materials Using Graph Theory

ACS Nano ◽  
2021 ◽  
Author(s):  
Drew A. Vecchio ◽  
Samuel H. Mahler ◽  
Mark D. Hammig ◽  
Nicholas A. Kotov
Keyword(s):  
Graph Theory ◽  
Structural Analysis

scholarly journals Logistics management of the rail connections using graph theory: the case of a public transportation company on the example of Koleje Dolnośląskie S.A.

2018 ◽  
Vol 10 (3) ◽  
pp. 7-22
Author(s):  
Paweł Sobczak ◽  
Ewa Stawiarska ◽  
Judit Oláh ◽  
József Popp ◽  
Tomas Kliestik
Keyword(s):  
Graph Theory ◽  
Structural Analysis ◽  
Public Transportation ◽  
Transportation Networks ◽  
Logistics Management ◽  
Simulation Methods ◽  
Southern Poland ◽  
Transport Services ◽  
Network Simulations ◽  
Simulation Results

Abstract The main purpose of the paper was the structural analysis of the connections network used by a railway carrier Koleje Dolnośląskie S.A. operating in southern Poland. The analysis used simulation methods. The analysis and simulation were based on graph theory, which is successfully used in analysing a wide variety of networks (social, biological, computer, virtual and transportation networks). The paper presents indicators which allow judging the analysed connections network according to an appropriate level of transport services. Simulation results allowed proposing some modifications for the improvement of the analysed connections network. The paper also demonstrates that graph theory and network simulations should be used as tools by transportation companies during the stage of planning a connections network.

scholarly journals Application of Linear and Nonlinear Graphs in Structural Synthesis of Kinematic Chains

1973 ◽  
Vol 95 (2) ◽  
pp. 525-532 ◽  
Author(s):  
M. Huang ◽  
A. H. Soni
Keyword(s):  
Mathematical Model ◽  
Graph Theory ◽  
Structural Analysis ◽  
Three Dimensional ◽  
Structural Synthesis ◽  
Kinematic Chains ◽  
Piston Cylinder ◽  
General Constraints ◽  
Analysis And Synthesis ◽  
Linear And Nonlinear

Using graph theory and Polya’s theory of counting, the present paper performs structural synthesis and analysis of planar and three-dimensional kinematic chains. The Section 2 of the paper develops a mathematical model that permits one to perform structural analysis and synthesis of planar kinematic chains with kinematic elements such as revolute pairs, cam pairs, springs, belt-pulley, piston-cylinder, and gears. The theory developed is applied to enumerate eight-link kinematic chains with these kinematic elements. The Section 3 of the paper develops a mathematical model that permits one to perform structural analysis and synthesis of multi-loop spatial kinematic chains with higher and lower kinematic pairs. The theory developed is applied to enumerate all possible two-loop kinematic chains with or without general constraints.

Structural Analysis and Mobility Test of Fourteen Links Kinematic Chain Using Graph Theory

2014 ◽  
Vol 592-594 ◽  
pp. 1165-1169
Author(s):  
Preeti Gulia ◽  
V.P. Singh
Keyword(s):  
Graph Theory ◽  
Structural Analysis ◽  
Incidence Matrix ◽  
Reliable Method ◽  
Kinematic Chain ◽  
Polynomial Equation ◽  
Degree Of Freedom ◽  
Mobility Test ◽  
Structural Problems ◽  
Algebraic Test

The present work is focused on the graph theory which is used for structural analysis of kinematic chain and identification of degree of freedom. A method based on graph theory is proposed in this paper to solve structural problems by using a suitable example of fourteen links kinematic chain. Purpose of this paper is to give an easy and reliable method for structural analysis of fourteen links kinematic chain. Here, a simple incidence matrix is used to represent the kinematic chain. The proposed method is applied for determining the characteristic polynomial equation of fourteen links kinematic chain. An algebraic test based on graph theory is also used for identifying degree of freedom of kinematic chain whether it is total, partial or fractionated degree of freedom.

scholarly journals On Fault-Tolerant Partition Dimension of Homogeneous Caterpillar Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Kamran Azhar ◽  
Sohail Zafar ◽  
Agha Kashif
Keyword(s):  
Absorption Spectrum ◽  
Graph Theory ◽  
Structural Analysis ◽  
Fault Tolerant ◽  
Chemical Compounds ◽  
Numerical Examples ◽  
Benzenoid Hydrocarbon ◽  
Partition Dimension ◽  
Hydrocarbon Molecules ◽  
Uv Absorption Spectrum

Metric-related parameters in graph theory have several applications in robotics, navigation, and chemical strata. An important such parameter is the partition dimension of graphs that plays an important role in engineering, computer science, and chemistry. In the context of chemical and pharmaceutical engineering, these parameters are used for unique representation of chemical compounds and their structural analysis. The structure of benzenoid hydrocarbon molecules is represented in the form of caterpillar trees and studied for various attributes including UV absorption spectrum, molecular susceptibility, anisotropy, and heat of atomization. Several classes of trees have been studied for partition dimension; however, in this regard, the advanced variant, the fault-tolerant partition dimension, remains to be explored. In this paper, we computed fault-tolerant partition dimension for homogeneous caterpillars C p ; 1 , C p ; 2 , and C p ; 3 for p ≥ 5 , p ≥ 3 , and p ≥ 4 , respectively, and it is found to be constant. Further numerical examples and an application are furnished to elaborate the accuracy and significance of the work.

Structural Analysis With Graphs

2020 ◽  
pp. 31-47
Keyword(s):  
Social Networks ◽  
Graph Theory ◽  
Social Network ◽  
Social Network Analysis ◽  
Structural Analysis ◽  
Network Analysis ◽  
Social Research ◽  
Analysis Methods

Graphs are mathematical formalisms that represent social networks very well. Analysis methods using graph theory have started to develop substantially along with the advancement of mathematics and computer sciences in recent years, with contributions from several disciplines including social network analysis. Learning how to use graphs to represent social networks is important not only for employing theoretical insights of this advanced field in social research, but also for the practical purposes of utilizing its mature and abundant tools. This chapter explores structural analysis with graphs.

scholarly journals Caveats: Numerical Requirements in Graph Theory Based Quantitation of Tissue Architecture

2000 ◽  
Vol 21 (2) ◽  
pp. 59-69 ◽  
Author(s):  
J. Sudbø ◽  
R. Marcelpoil ◽  
A. Reith
Keyword(s):  
Graph Theory ◽  
Structural Analysis ◽  
Oral Mucosa ◽  
Voronoi Diagram ◽  
Structural Features ◽  
Grey Level ◽  
Tissue Architecture ◽  
Cell Nuclei ◽  
Centre Of Gravity ◽  
Number Of Cells

Graph theory based methods represent one approach to an objective and reproducible structural analysis of tissue architecture. By these methods, neighborhood relations between a number of objects (e.g., cells) are explored and inherent to these methods are therefore certain requirements as to the number of objects to be included in the analysis. However, the question of how many objects are required to achieve reproducible values in repeated computations of proposed structural features, has previously not been adressed specifically.After digitising HE stained slides and storing them as grey level images, cell nuclei were segmented and their geometrical centre of gravity were computed, serving as the basis for construction of the Voronoi diagram (VD) and its subgraphs. Variations in repeated computations of structural features derived from these graphs were related to the number of cell nuclei included in the analysis.We demonstrate a large variation in the values of the structural features from one computation to another in one and the same section when only a limited number of cells (100–500) are included in the analysis. This variation decreased with increasing number of cells analyzed. The exact number of cells required to achieve reproducible values differ significantly between tissues, but not between separate cases of similar lesions. There are no significant differences between normal and malignantly changed tissues in oral mucosa with respect to how many cells must be included.For graph theory based analysis of tissue architecture, care must be taken to include an adequate number of objects; for some of the structural features we have tested, more than 3000 cells.

scholarly journals Structural Analysis of Network Connections of Koleje Małopolskie sp. z o.o. as a Significant Element of the Management of the Transport Company

2019 ◽  
pp. 117-145
Author(s):  
Paweł Sobczak
Keyword(s):  
Graph Theory ◽  
Structural Analysis ◽  
Public Transport ◽  
Social Space ◽  
Simulation Method ◽  
Service Company ◽  
Significant Element ◽  
Current State ◽  
Network Connections

Public transport is one of the most important elements of the economy and social space development in which it is located. Issues related to its proper organisation are very often the responsibility of transport companies, which must operate and carry out their activities within the principles of the economy, that is, the principles of managing a service company. An important element of an efficient and effective functioning of a transport company is the quality of the provided services. An element significantly affecting the quality of the services offered is, inter alia, an appropriately organised network of connections offered by the carrier. This network in an efficient and interference-resistant manner must facilitate transport in a given area. In the article, using the graph theory and the simulation method, the structure of network connections of a railway carrier operating in the Małopolska region (Koleje Małopolskie sp. z o.o.) in Poland was analysed. The aim of the analysis was to obtain information about the current condition and parameters of the network offered by the carrier. Theconducted analysis made it possible to assess the current state as well as within the conducted research and it proposed to modify the existing network of connections in order to improve its parameters. The carrier’s network is used, inter alia, to co-create public transport in the region, and the structure of the connections network and its appropriate planning can have a significant impact on the functioning of the company.

Detection of Isomorphism Between Planar Kinematic Chains

1987 ◽  
Author(s):  
L. K. Patel ◽  
A. C. Rao
Keyword(s):  
Graph Theory ◽  
Structural Analysis ◽  
Efficient Method ◽  
Computational Effort ◽  
New Method ◽  
Structural Topology ◽  
Single Degree Of Freedom ◽  
Kinematic Chains ◽  
Single Degree ◽  
Analysis And Synthesis

Abstract Structural analysis and synthesis of linkages is a very important aspect. Detection of isomorphism (equivalent structural topology) is essential to determine structurally distinct chains. Some methods to detect distinct chains and mechanisms have already been developed. These methods besides being falliable, require enormous computational effort and as such necessitate development of an easy and efficient method. This paper presents a new method based on graph theory, for detection of isomorphism among kinematic chains. A probability scheme is attached with the chains and relative loop positions are determined for the chains having identical probability schemes. Isomorphism is detected between planar kinematic chains having single degree of freedom.

Some Applications of Graph Theory to the Structural Analysis of Mechanisms

1967 ◽  
Vol 89 (1) ◽  
pp. 153-158 ◽  
Author(s):  
L. Dobrjanskyj ◽  
F. Freudenstein
Keyword(s):  
Graph Theory ◽  
Structural Analysis ◽  
Incidence Matrix ◽  
Mechanical Systems ◽  
Kinematic Chains ◽  
Computerized Method ◽  
Spatial Mechanisms ◽  
Structural Identity ◽  
Computer Aided ◽  
Systematic Enumeration

Concepts in graph theory, which have been described elsewhere [2, 4, 6] have been applied to the development of (a) a computerized method for determining structural identity (isomorphism) between kinematic chains, (b) a method for the automatic sketching of the graph of a mechanism defined by its incidence matrix, and (c) the systematic enumeration of general, single-loop constrained spatial mechanisms. These developments, it is believed, demonstrate the feasibility of computer-aided techniques in the initial stages of the design of mechanical systems.

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