History of Graph Theory

2013 ◽  
pp. 31-51 ◽  
Author(s):  
Robin Wilson
Keyword(s):  
Graph Theory ◽  
History Of

Graph Applications in Chemoinformatics and Structural Bioinformatics

2011 ◽  
pp. 386-420
Author(s):  
Eleanor Joyce Gardiner
Keyword(s):  
Graph Theory ◽  
Molecular Graph ◽  
Structural Bioinformatics ◽  
Three Dimensions ◽  
Chemical Graph ◽  
Labeled Graph ◽  
3D Space ◽  
Chemical Graph Theory ◽  
Computer Representation ◽  
History Of

The focus of this chapter will be the uses of graph theory in chemoinformatics and in structural bioinformatics. There is a long history of chemical graph theory dating back to the 1860’s and Kekule’s structural theory. It is natural to regard the atoms of a molecule as nodes and the bonds as edges (2D representations) of a labeled graph (a molecular graph). This chapter will concentrate on the algorithms developed to exploit the computer representation of such graphs and their extensions in both two and three dimensions (where an edge represents the distance in 3D space between a pair of atoms), together with the algorithms developed to exploit them. The algorithms will generally be summarized rather than detailed. The methods were later extended to larger macromolecules (such as proteins); these will be covered in less detail.

scholarly journals Graphic representation of open and distance education history

2017 ◽  
Vol 7 (3) ◽  
pp. 92-98
Author(s):  
Filiz Mete ◽  
Serife Buyukkose ◽  
Ozlem Cakir ◽  
Ummugulsum Candeger
Keyword(s):  
Distance Education ◽  
Graph Theory ◽  
Education System ◽  
Interactive Video ◽  
Instructional Materials ◽  
Education History ◽  
Turkish Republic ◽  
Big Picture ◽  
History Of ◽  
Distance Education System

Nowadays, learning and instruction take place independent of time and space through the distance education system,wherein courses are conducted completely online through network technologies using interactive video -based instructional materials. This study examines the open and distance education system that was a part of the history of education in the Turkish republic first at universities, and then in high sch ools and secondary schools. It is aimed to narrate the history of open and distance education using graph theory trees in order to provide a better understanding of this process. Within this context, the project YAYÇEP may be mentioned. Historical developments can be narrated in a chronological order through graph theory trees, and this makes it possible to see the big picture. Open and distance education is discussed, historical information is given and, finally, a graph theory tree drawn using the graph theory is used to explain the topic.Keywords: Distance education, open education, graph theory, the history of distance education.

Graph Applications in Chemoinformatics and Structural Bioinformatics

2013 ◽  
pp. 1126-1157 ◽  
Author(s):  
Eleanor Joyce Gardiner
Keyword(s):  
Graph Theory ◽  
Molecular Graph ◽  
Structural Bioinformatics ◽  
Three Dimensions ◽  
Chemical Graph ◽  
Labeled Graph ◽  
3D Space ◽  
Chemical Graph Theory ◽  
Computer Representation ◽  
History Of

The focus of this chapter will be the uses of graph theory in chemoinformatics and in structural bioinformatics. There is a long history of chemical graph theory dating back to the 1860’s and Kekule’s structural theory. It is natural to regard the atoms of a molecule as nodes and the bonds as edges (2D representations) of a labeled graph (a molecular graph). This chapter will concentrate on the algorithms developed to exploit the computer representation of such graphs and their extensions in both two and three dimensions (where an edge represents the distance in 3D space between a pair of atoms), together with the algorithms developed to exploit them. The algorithms will generally be summarized rather than detailed. The methods were later extended to larger macromolecules (such as proteins); these will be covered in less detail.

Basics of Graph Theory

2013 ◽  
pp. 1-13
Author(s):  
Payman Biukaghazadeh
Keyword(s):  
Graph Theory ◽  
History Of

This chapter introduces preliminary definitions required in the rest of this book. It is recommended to read this chapter before starting the rest of the book. At the first section of this chapter the history of graph theory is described. Well-known problems, such as Hamilton’s game and Euler’s paths and cycles, are introduced. Finally, terminologies and notations are described.

Introducing Graphs

2017 ◽  
Author(s):  
Arthur Benjamin ◽  
Gary Chartrand ◽  
Ping Zhang
Keyword(s):  
Graph Theory ◽  
Mathematical Structure ◽  
Color Problem ◽  
Bridge Problem ◽  
The World ◽  
History Of

This chapter provides an introduction to graphs, a mathematical structure for visualizing, analyzing, and generalizing a situation or problem. It first consider four problems that have a distinct mathematical flavor: the Problem of the Five Princes, the Three Houses and Three Utilities Problem, the Three Friends or Three Strangers Problem, and the Job-Hunters Problem. This is followed by discussion of four problems that are not only important in the history of graph theory, but which led to new areas within graph theory: the Königsberg Bridge Problem, the Four Color Problem, the Polyhedron Problem, and the Around the World Problem. The chapter also explores puzzles and problems involving chess that have connections to graph theory before concluding with an overview of the First Theorem of Graph Theory, which is concerned with what happens when the degrees of all vertices of a graph are added.

Thermal Modeling in Metal Additive Manufacturing Using Graph Theory: Experimental Validation With Laser Powder Bed Fusion Using In Situ Infrared Thermography Data

2020 ◽  
Vol 142 (12) ◽  
Author(s):  
M. Reza Yavari ◽  
Richard J. Williams ◽  
Kevin D. Cole ◽  
Paul A. Hooper ◽  
Prahalada Rao
Keyword(s):  
Finite Element ◽  
Graph Theory ◽  
Additive Manufacturing ◽  
Surface Temperature ◽  
Theory Approach ◽  
Powder Bed ◽  
Temperature Trends ◽  
History Of ◽  
Made In

Abstract The objective of this work is to provide experimental validation of the graph theory approach for predicting the thermal history of additively manufactured parts. The graph theory approach for thermal modeling in additive manufacturing (AM) was recently published in these transactions. In the present paper, the graph theory approach is validated with in situ infrared thermography data in the context of the laser powder bed fusion (LPBF) additive manufacturing process. We realize the foregoing objective through the following four tasks. First, two kinds of test shapes, namely, a cylinder and cone, are made in two separate builds on a production-type LPBF machine (Renishaw AM250); the material used for these tests is stainless steel (SAE 316L). The intent of both builds is to influence the thermal history of the part by controlling the cooling time between the melting of successive layers, called the interlayer cooling time (ILCT). Second, layer-wise thermal images of the top surface of the part are acquired using an in situ a priori calibrated infrared camera. Third, the thermal imaging data obtained during the two builds is used to validate the graph theory-predicted surface temperature trends. Fourth, the surface temperature trends predicted using graph theory are compared with results from finite element (FE) analysis. The results substantiate the computational advantages of the graph theory approach over finite element analysis. As an example, for the cylinder-shaped test part, the graph theory approach predicts the surface temperature trends to within 10% mean absolute percentage error (MAPE) and approximately 16 K root mean squared error (RMSE) relative to the surface temperature trends measured by the thermal camera. Furthermore, the graph theory-based temperature predictions are made in less than 65 min, which is substantially faster than the actual build time of 171 min. In comparison, for an identical level of resolution and prediction error, the finite element approach requires 175 min.

scholarly journals Graph Routing Problem Using Euler’s Theorem and Its Applications

2019 ◽  
Author(s):  
Hashnayne Ahmed
Keyword(s):  
Graph Theory ◽  
Social Science ◽  
Routing Protocols ◽  
Routing Problem ◽  
Euler’S Theorem ◽  
Bridge Problem ◽  
Eulerian Circuit ◽  
History Of ◽  
Proof Techniques ◽  
Modern Era

In this modern era, time and cases related to time is very important to us. For shortening time, Eulerian Circuit canopen a new dimension. In computer science, social science and natural science, graph theory is a stimulating space for thestudy of proof techniques. Graphs are also effective in modeling a variety of optimization cases like routing protocols, networkmanagement, stochastic approaches, street mapping etc. Konigsberg Bridge Problem has seven bridges linked with four islandsdetached by a river in such a way that one can’t walk through each of the bridges exactly once and returning back to thestarting point. Leonard Euler solved it in 1735 which is the foundation of modern graph theory. Euler’s solution forKonigsberg Bridge Problem is considered as the first theorem of Graph Theory which gives the idea of Eulerian circuit. It canbe used in several cases for shortening any path. From the Konigsberg Bridge Problem to ongoing DNA fragmentationproblem, it has its applications. Aiming to build such a dimension using Euler’s theorem and Konigsberg Bridge Problem, thispaper presents about the history of remarkable Konigsberg Bridge Problem, Euler’s Explanation on it, an alternativeexplanation and some applications to Eulerian Circuit using graph routing and Fortran Coding of it.

scholarly journals Graph Routing Problem Using Euler’s Theorem and Its Applications

2019 ◽  
Author(s):  
Hashnayne Ahmed
Keyword(s):  
Graph Theory ◽  
Social Science ◽  
Routing Protocols ◽  
Routing Problem ◽  
Euler’S Theorem ◽  
Bridge Problem ◽  
Eulerian Circuit ◽  
History Of ◽  
Proof Techniques ◽  
Modern Era

In this modern era, time and cases related to time is very important to us. For shortening time, Eulerian Circuit canopen a new dimension. In computer science, social science and natural science, graph theory is a stimulating space for thestudy of proof techniques. Graphs are also effective in modeling a variety of optimization cases like routing protocols, networkmanagement, stochastic approaches, street mapping etc. Konigsberg Bridge Problem has seven bridges linked with four islandsdetached by a river in such a way that one can’t walk through each of the bridges exactly once and returning back to thestarting point. Leonard Euler solved it in 1735 which is the foundation of modern graph theory. Euler’s solution forKonigsberg Bridge Problem is considered as the first theorem of Graph Theory which gives the idea of Eulerian circuit. It canbe used in several cases for shortening any path. From the Konigsberg Bridge Problem to ongoing DNA fragmentationproblem, it has its applications. Aiming to build such a dimension using Euler’s theorem and Konigsberg Bridge Problem, thispaper presents about the history of remarkable Konigsberg Bridge Problem, Euler’s Explanation on it, an alternativeexplanation and some applications to Eulerian Circuit using graph routing and Fortran Coding of it.

scholarly journals Review on Chemical Graph Theory and Its Application in Computer-Assisted Structure Elucidation

2021 ◽  
Author(s):  
Mehmet Aziz Yirik ◽  
Kumsal Ecem Colpan ◽  
Saskia Schmidt ◽  
Maria Sorokina ◽  
Christoph Steinbeck
Keyword(s):  
Graph Theory ◽  
Data Structures ◽  
Computer Assisted ◽  
Structure Property ◽  
Chemical Graph ◽  
Chemical Structures ◽  
Chemical Graph Theory ◽  
Structure Activity ◽  
History Of ◽  
Computer Assisted Structure Elucidation

The chemical graph theory is a subfield of mathematical chemistry which applies classic graph theory to chemical entities and phenomena. Chemical graphs are main data structures to represent chemical structures in cheminformatics. Computable properties of graphs lay the foundation for (quantitative) structure activity and structure property predictions - a core discipline of cheminformatics. It has a historic relevance for natural sciences, such as chemistry, biochemistry and biology, and is in the heart of modern disciplines, such as cheminformatics and bioinformatics. This review first covers the history of chemical graph theory, then provides an overview of its various techniques and applications for CASE, and finally summarises modern tools using chemical graph theory for CASE.

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