application of graph theory in engineering

4. graph theory by narsing deo – Ebook download as PDF File .pdf) or read book online. [4]Narasingh Deo, Graph theory with applications to engineering and computer science, Prentice Hall of India, (1990). Graph Theory Graph theory and its engineering applications (eBook, 1997 ... Keywords:- graph theory, Konigsberg bridge problem, Eulerian circuit. Graph Theory with Applications to Engineering and Computer ... Applications of Graph Theory. This work explores the following applications of graph theory to plasma chemical reaction engineering: assembly of a weighted directional graph with the key addition of reaction nodes, from a published set of reaction data for air; graph visualisation for probing the reaction network for potentially useful or problematic reaction pathways; running Dijkstra’s algorithm … • If it has been used, then choose the next least … The subject of graph theory had its beginnings in recreational problems, but it was grown into significant area of mathematical research with application in chemistry, computer science, and social science. Applications in Physics Graph theory is also used in the eld of physics. 19D081TG - Graph Theory and Applications in Electrical Engineering and Computing. Graph Theory is just a beautiful part of mathematics. Real-Life Applications of Graph [5] ORE, … Molecular species are naturally represented by graphs, which are identified by their vertices and edges where vertices are atom types and edges are bonds. Graph Theory The mechanism is generated using a set of reaction patterns (sub-graphs). Graph Theory with Applications to Engineering and Computer ... Section 3 illustrates how graph theory is utilised in various domain of engineering applications. Graph Theory c h i j g e d f b Figure 5.1 An example of a graph with 9 nodes and 8 edges. A short summary of this paper. Graph Theory, which studies the properties of graphs, has been widely accepted as a core subject in the knowledge of computer scientists. Its product suite reflects the philosophy that given great tools, people can do great things. This outstanding introductory treatment of graph theory and its applications has had a long life in the instruction of advanced undergraduates and graduate students in all areas that require knowledge of this subject. This Paper. Graph Theory with Applications to Engineering and Computer Graph theory and its engineering applications. In addition to that, Graph theoretic concepts have many applications in network engineering, such as connectivity, data The first nine chapters constitute an excellent overview, requiring only some knowledge of set theory and matrix algebra. Choose from Same Day Delivery, Drive Up or Order Pickup. The discourse is just enough to whet the appetite for more advanced study, while remaining very accessible. The mechanism is generated using a set of reaction patterns (sub-graphs). Alterations in FC within the whole brain were … Graph Theory with Applications to Engineering and Computer Science: : Deo, Narsingh: Books Dual graphs were Top Applications. Develop a survey to determine whether people are aware of the mathematics in graph theory behind the applications they use. b. Algorithms and graph theory: The most important role of graph theory in computer applications is the development of graph algorithms. International journal of Application of Application or innovation in Engineering and Management Volume 1, issue 2 And October 2012. In this paper, an application description of the graph is presented to find the shortest path and circuit network. It is a popular subject having its applications in computer science, information technology, biosciences, mathematics, and linguistics to name a few. Graph Theory with Applications to Engineering and Computer Science (Dover Books on Mathematics) In electrical engineering, graph theory is applied in communication networks and coding theory. • Text: • C.L. Maybe you have knowledge that, people have look numerous times for their chosen novels like this application of graph theory in engineering, but end up in malicious downloads. several algorithms are used to solve problems that are modeled in the form of graphs. Computer Science. Graph Theory with Applications to Engineering and Computer Science (Dover Books on Mathematics) [Deo, Narsingh] on Amazon.com. It is a popular subject having its applications in computer science, information technology, biosciences, mathematics, and linguistics to name a few. A major theme of the book is electrical network theory. Some results, 3. Expect More. Acquiring knowledge of selected topics of graph theory necessary in research in modern discrete mathematics and its applications in computer science and electrical engineering. This are entities such as Users, Pages, Places, Groups, Comments, Photos, Photo Albums, Stories, Videos, Notes, Events and so forth. About Call for Papers Registration Conference Programme. An overview of the applications of graph theory in heterogeneous fields to some extent is given, which mainly focuses on the computer science applications that uses graph theoretical concepts and role of labeling in expanding the utility of this channel assignment process in communication networks. A survey of applications, 4. application of graph theory in engineering is understandable in our digital library an online access to it is set as public suitably you can download it instantly. applications of graph theory particularly in computer science. In briefly, graph theory has its unique impact in various fields and is growing large now a days. and graph/network theory. Then we have more on types of graphs and general classes of applications, followed by a chapter that discusses computer solution of many applications of graph theory. Algorithms and graph theory: The major role of graph theory in computer applications is the development of graph algorithms. Abstract: In this paper, the research has been focus on application of graph theory in various field of Science & Engineering like Because of its inherent simplicity, graph theory has a wide range of applications in engineering, and in physical sciences. Mathematical education at the undergraduate level. This introductory text provides an introduction to the theory of graph spectra and a short survey of applications of graph spectra. Set up a giveaway. These algorithms are used to solve the graph theoretical concepts which intern used to solve the corresponding computer science application problems. Network Engineering: In [1] and [5] author have explained an application of graph in networking. Further applications of graph theory in civil engineering, involving highway route and pier construction planning, are outlined by Chachra et al. 5. Software engineers further apply graph theory in object-oriented programming with the analysis, design and implementation of systems employing classes as modules. Application Of Graph Theory In Engineering Application Of Graph Theory In Engineering As recognized, adventure as competently as experience practically lesson, amusement, as skillfully as promise can be gotten by just checking out a book application of graph theory in engineering as well as it is not directly done, you could tolerate Objective: To determine brain functional connectivity (FC), based on the graph theory, in individuals with psychogenic nonepileptic seizures (PNES), in order to better understand the mechanisms underlying this disease. graph theory, and is generally regarded as the origin of topology Vanermonde: The knights tour problem Cauchy and L’Hullier: Relationships between faces, edges, and vertices of convex polyhedrons Study of pair-wise relationships between objects Graphs are the parent family to a variety of topologies: directed graphs Graph Theory Applications "This book put[s] together the theory and applications of graphs in a single, self-contained, and easily readable volume . The subsequent section analyses the applications of graph theory especially in computer science. . You could not single-handedly going considering book buildup or library or borrowing from your connections to retrieve them. The current, voltage and resistance on a circuit can be drawn by using graph theory concept. International journal of Application of Application or innovation in Engineering and Management Volum 1, issu 2 And October 2012. These applications are illustrated with selected examples. of the use and applications of graph theoretic concept in modelling and analysis of systems in different fields. Overview Graph Applications. Molecular species are naturally represented by graphs, which are identified by their vertices and edges where vertices are atom types and edges are bonds. Learning will be simple and this book would be a good tool to have an in-depth knowledge on the subject. This text gives a reasonably deep account of material closely related to engineering applications. 5 Graph Theory Informally, a graph is a bunch of dots and lines where the lines connect some pairs of dots. In brief, graph theory has its unique impact in various fields and is growing large now a days. Similar Items. • Evaluate some real time problems using concepts of graph theory. 14 In this paper we present the application of a k-shortest disjoint paths algorithm for multiple-object 15 tracking using a motion-based optimization based on dual graphs. Some of them are given below: 1. This beginner course covers the fundamental concepts in graph theory and some of its applications. Graphs can be used to model many types of relations and processes in physical, biological, social and information systems. Graph Theory with Applications to Engineering & Computer Science NARSINGH DEO Millican Chair Professor, Dept. Facebook's Graph API is perhaps the best example of application of graphs to real life problems. Applications of Graph Data Structure. [6]. Formally, a graph is a pair of sets (V, E),where Vis the set of vertices and Eis the set of edges, connecting the pairs of vertices. Take a look at the following graph: In the above graph, V = {a, b, c, d, e} E = {ab, ac, bd, cd, de} Applications of Graph Theory Graph theory has its applications in diverse fields of engineering − These algorithms are Read Online 62.2 MB Download. Not only Computer Science is heavily based on Graph Theory. SHORT HISTORY OF GRAPH/NETWORK THEORY CLOSELY RELATED TO TOP-ICS OF THIS PAPER An electrical circuit is a typical example of a net-work, and the connection structure of such circuit ele-ments as resistors, capacitors, inductors, and/or volt-age sources is a typical example of a graph. Methodology Ten everyday scenarios with an underlying application of graph theory: 1. River Edge, NJ. We present an application of the chemical graph theory approach for generating elementary reactions of complex systems. Each part is divided into chapters, each concluding with a summary and a nice collection of exercises . Read Online 62.2 MB Download. graph theory and their applications in computer science to demonstrate the utility of graph theory. Representative examples for the usefulness of graph theory on OO systems based on recent research results are presented in this paper. Read reviews and buy Graph Theory and Its Engineering Applications - (Advanced Electrical and Computer Engineering) by Wai-Kai Chen (Hardcover) at Target. You may have already requested this item. Selected Edition Notes Includes bibliographical references (p. 671-683) and index. Pages with related products. Graph Theory with Applications to Engineering and Computer Science. 0 Full PDFs related to … Download the App as a reference material & digital book for Computer science engineering, IT, software engineering programs & Mathematics & Combinatorial Theory degree courses. Graph Theory and its Applications. Graphic methods , Graph theory , Electric engineering , Electrical engineering. The Department of Mathematics, School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore, is organizing an “International Conference on Graph Theory and its Applications” during December 16-19, 2020. Numerous Graph Theory is used in vast area of science and technologies. Fractal Graph is the famous graph which has self-similarity property included it. [1] Application of graph theory in computer science an overview by S G Shrinivas, S Vetrivel and Dr N M Elango, International journal of engineering science and technology , vol-2(9), 2010,4610-4621. graphical representation which helps us understand many of their properties. ORE, O, theory of graphs American mathematical society providence R.I. 1962. For example, in the case of link prediction in a social network, one might want to encode pairwise properties between nodes, such as relationship strength or the number of common friends. This outstanding introductory treatment of graph theory and its applications has had a long life in the instruction of advanced undergraduates and graduate students in all areas that require knowledge of this subject. The purpose of this paper is to connect graphs with engineering and electrical subjects. To download Graph Theory with Applications to Engineering and Computer Science, eBook, you should follow the button under and save the ebook or have access to additional information which might be have conjunction with GRAPH THEORY WITH APPLICATIONS TO ENGINEERING AND COMPUTER SCIENCE, book. electrical network analysis. accumulate and study several research papers related to the graph algorithms and its application in the field of software engineering. Graph Theory - Introduction. Many algorithms are used to solve problems that are modeled in the form of graphs. use the graph theory concept and We techniques that we have developed to study electrical networks. Related Subjects: (2) Graph theory. A graph is a non-linear data structure, which consists of vertices (or nodes) connected by edges (or arcs) where edges may be directed or undirected. Basic notions, 2. (1979). Different concepts involved in graph theory and their applications in computer science to demonstrate the utility of graph theory are explored to project the idea ofgraph theory and to demonstrate its objective and importance inComputer science engineering. Subjects. Getting the books graph theory with applications to engineering and computer science narsingh deo now is not type of inspiring means. [Reza Zanjirani Farahani; Elnaz Miandoabchi;] -- "This book presents traditional and contemporary applications of graph theory in the areas of industrial engineering, management science and applied operations research"--Provided by publisher. Facebook's Graph API is perhaps the best example of application of graphs to real life problems. An example is shown in Figure 5.1. Methods: Twenty-three patients with PNES and twenty-five healthy control subjects were examined. Our digital library saves in complex countries, allowing you to get the most less Showing of 4 reviews. [2] N. Deo, “Graph theory with applications to Engineering and computer science”, Prentice Hall of India, 1999. 2. • Now, consider the remaining (V-1) vertices one by one and do the following-• Color the currently picked vertex with the lowest numbered color if it has not been used to color any of its adjacent vertices. 2. Graph Theory and Its Engineering Applications. Graphs are extremely useful in modeling systems in physical sciences and engineering problems, because of their intuitive diagrammatic nature. This text gives a reasonably deep account of material closely related to engineering applications. We then go on to the major application of this chapter, which involves the design of urban traffic networks. Survey of other Applications. The Basics of Graph Theory. Free standard shipping with $35 orders. Graph Theory with Applications to Engineering and Computer Science (Dover Books on Mathematics) [Narsingh Deo] on *FREE* shipping on. This outstanding introductory treatment is geared toward advanced undergraduates and graduate students in all areas that require knowledge of graph theory. These applications are presented especially to project the idea of graph theory and to demonstrate its objective and importance in computer science engineering. So is Object-Oriented (OO) software engineering, which deals with the analysis, design and … And graphs are special cases of networks, with only a single type of edge between vertices. Be the first. Graph Theory and related computational techniques have been applied to a wide range of problems in process design and analysis to facilitate visualization, formulation, computation and interpretation. Graph Theory With Applications To Engineering And Computer Science by Narsingh Deo / 1974 / English / PDF. The dots are called nodes (or vertices) and the lines are called edges. Applications of graph in the various engineering field 2.1. Algorithms and graph theory: The most important role of graph theory in computer applications is the growth of graph algorithms. described with graph theory; that is, as sets of vertices and their connections with edges. In computer science graph theory is used for the study of algorithms like: Graphs are used to define the flow of computation. A graph is a pair of sets (V,E) where V is the set of vertices and E is the set of edges. graphical representation which helps us understand many of their properties. The Graph API is a revolution in large-scale data provision. NarsinghDeo, Graph theory with Applications to Engineering & CS, PHI Alan Gibbons, Algorithmic Graph theory, Cambridge University Press Jeffrey J. Narasingh Deo, “Graph theory with applications to engineering and computer science”, Prentice Hall of India, 1990. 2. The subsequent section analyses the applications of graph theory especially in computer science. Electrical engineering -- Graphic methods. Sukrita Saha. There are a lot of applications of Graph Theory in Operational Research, Combinatorial Optimization, Bioinformatics. line connecting two nodes. These are the most important graph applications: Social networks: A social network is by definition, well, a network. Chemical and biochemical reaction engineering contains many complicated mechanisms. Computer and software engineers apply graph theory as algorithms and computations. About. E consists of pairs of elements of V. That means that for two points v and w in V the pair (v,w) is contained in E if there is an edge between v and w in the graph. First published in 1997. In Computer science graphs are used to represent the flow of computation. In fact, a graph can be used to represent almost any physical situation involving discrete objects and the relationship among them. When we want to show throw of current in circuits then we can use directed graphs. Fingerprint classification using graph theory. Confirm this request. APPLICATIONS OF GRAPHS. [3]S.G.Shrinivas, S.Vetrivel and N.M.Elango, Applications of graph theory in computer science an overview, International Journal of Engineering Science and Technology, 2(9)(2010), 4610-4621. Follow the Author. Topics like directed-graph solutions of linear equations, topological analysis of linear systems, state equations, rectangle dissection and layouts, and network flows are included. . Add tags for "Graph theory and its engineering applications". Electrical Engineering, M.I.T., July 1956, in partial fulfill-ment of the requirements for the degree of Doctor of Science. [4] Application of graph theory in communication networks by Suman Deswal and Anita Singhrova. Graph Theory: Applications to Chemical Engineering and Chemistry Sunil Jayant Kulkarni Datta Meghe College of Engineering, Airoli, Navi Mumbai, Maharashtra, India _____ ABSTRACT Current review summarizes research and studies on graph theory. The paper is organised as follows: After this introduction, Section 2 gives a background of graph theory concept. *FREE* shipping on qualifying offers. This are entities such as Users, Pages, Places, Groups, Comments, Photos, Photo Albums, Stories, Videos, Notes, Events and so forth. Preface to Graph Theory PDF Book. Applications of Graph Spectra: An Introduction to the Literature (D. Cvetkovi¶c). A figure was concluded at the end of the review to brief the importance of discrete-math developing the relationship between computer engineering in general and graph theory’s role in developing machine learning in particular. ... A graph is a set of objects called vertices or nodes, joined by lines known as edges. A graph is a representation of a system that uses two basic elements of vertices and edges, a node represented by a circle and edge represented by a line connecting two nodes. This is an entirely simple means to specifically acquire lead by on-line. raphs are considered as an excellent modeling tool which is used to model many type of relations … Graph Theory can model and study many real-world problems and is applied in a wide range of disciplines. Web graphs: The web is a huge collection of documents pointing to each other via hyperlinks. Without further ado, let us Application of Graph Theory in Various Field of Applied Science & Engineering O. M. Teraiya Senior Assistant Professor & Head, Atmiya University, Rajkot 360005, Gujarat, India. Graphs are used to represent networks of communication. Thus, graph theory has more practical application Event Details. The last two decades have witnessed an upsurge of interest and activity in graph theory, particularly … A graph is a mathematical structure used to model relationships between the objects in a set of objects. Graph theory for operations research and management : applications in industrial engineering. Narsingh deo graph theory pdf download: In a recent time it has been observed that there is a massive growth in the field of digitalization and that leads to rise in demand and interest in the field of graph theory. Graph theory is widely used in every field of engineering. Students learn graph theory vocabulary, as well as engineering applications of graph theory. Pay Less. The basics of graph theory are pretty simple to grasp, so any text ... to engineering and computer science) by Narsingh Deo is a nice book. The app is a complete free handbook of Graph Theory which covers important topics, notes, materials & news on the course. A First Course in Graph Theory. Series Advanced series in electrical and computer engineering ;, vol. Graph Theory and Pokémon; Generating Parametric Curves from 2-D Data using Discrete Fourier Transforms ... is the leading provider of high-performance software tools for engineering, science, and mathematics. . GRAPHS • Graph theory has turned out to be a vast area with innumerable applications in the field of social networks , data organization , communication network and so on…. There are four sections: 1. Read Book Application Of Graph Theory In EngineeringApplication Of Graph Theory In Engineering Thank you very much for reading application of graph theory in engineering. Our digital library saves in complex countries, allowing you to get the most less Graph theory with application to engineering and computer science Narshing Deo. On The Graph API, everything is a vertice or node. Keywords Graphs, connectivity, constraints, graph coloring, graph drawing 1. The most important role of graph theory in computer applications is the growth of graph algorithms. Perri Mehonen, Janne Riihijarvi, Marina Petrova, “Automatic Channel allocation for small wireless area networks … Abstract Our object is threefold: to develop a basic theory of flow graphs; to extend their known application to electrical networks; and … PDF Free Download|Graph Theory with Applications to Engineering and Computer Science by Narsingh Deo . It has of course uses in social sciences, in linguistics and in numerous other areas. It represents a major application of digraphs and networks. Get this from a library! • We have considered here 1.Dijkstra’s algorithm 2. 1. Many Introduction A graph G consists of a set V called the set of points (nodes, vertices) of the graph and a set of edges such that each edge e E is associated with Download CS6702 Graph Theory and Applications Lecture Notes, Books, Syllabus Part-A 2 marks with answers CS6702 Graph Theory and Applications Important Part-B 16 marks Questions, PDF Books, Question Bank with answers Key.. Download link is provided for Students to download the Anna University CS6702 Graph Theory and Applications Lecture Notes,SyllabusPart A 2 marks … In this paper, an application description of the graph is presented to find the shortest path and circuit network. then survey how graph algorithms are used in different phases of software engineering, negotiate different approaches, and then specify a preliminary set of solution . In the domain of mathematics and computer science, graph theory is the study of graphs that concerns with the relationship among edges and vertices. The field of mathematics plays vital role in various fields. . Graph Theory With Applications To Engineering And Computer Science by Narsingh Deo. the fundamentals of graph theory are presented in a very accessible way . Download Download PDF. Engineering Connection Graph theory is the study of graphs and is applicable in computer science, mathematics and engineering. 1 Computer Science. Graphs are used to define the flow of computation. ... 2 Electrical Engineering. In Electrical Engineering, graph theory is used in designing of circuit connections. ... 3 Linguistics. ... 4 Physics and Chemistry. ... 5 Computer Network. ... 6 Social Sciences. ... 7 Biology. ... 8 Mathematics. ... 9 General. ... Graph Theory 1 In the domain of mathematics and computer science, graph theory is the study of graphs that concerns with the relationship among edges and vertices. [5]. Graph Coloring Graph Theory, Applications and Combinatorics Greedy Algorithm • Color first vertex with the first color. Application of Graph Theory to OO Software Engineering Alexander Chatzigeorgiou Nikolaos Tsantalis George Stephanides Department of Applied Informatics, University of Macedonia 156 Egnatia str., 54006 Thessaloniki, Greece Tel: +30 2310891886 achat@uom.gr, nikos@java.uom.gr, steph@uom.gr ABSTRACT . Graph theory has its applications in diver se fields of engineering: Electrical Engineering – The concepts of graph theory is used extensively in des igning circuit connections. Liu, Elements of Discrete Mathematics, Tata McGraw Hill, 2nd Edition, 2000. On The Graph API, everything is a vertice or node. . Graph theory and its engineering applications This edition was published in 1997 by World Scientific in Singapore, . In 1845, The first nine chapters constitute an excellent overall introduction, requiring only some knowledge of set theory and matrix algebra. On Applying Graph Theory to ILP Analysis by Raúl Durán, Rafael Rico Department of Computer Engineering, Universidad de Alcalá, Spain(2005) 4-graph application to data structures by V. manjula (2012) On the application of graph theory to computer data structure by R. Williams. Please select Ok if you would like to proceed with this request anyway. Graph theory is a very interesting topic mathematics due to numerous in applications in various fields especially computer and in electrical engineering. For my personal clasification I have separated the tasks, which you can solve using Graph Theory into two groups: Graph Theory With Applications To Engineering And Computer Science by Narsingh Deo / 1974 / English / PDF. Each vertex is … Each vertex is … The remaining six chapters are more advanced and provide material for courses in a variety of … … Full PDF Package Download Full PDF Package. Graph theory is widely used in every field of engineering. The first nine chapters constitute an excellent overall introduction, requiring only some knowledge of set theory and matrix algebra. graph theory, after that I summarizes the methods that are adopted to find Euler path and Euler cycle. application of graph theory in engineering is understandable in our digital library an online access to it is set as public suitably you can download it instantly. A graph can be drawn in the plane. The Graph API is a revolution in large-scale data provision. An algebraic interlude relates graphs to vector spaces and matrices, the latter because computer manipulation often depends on representing a graph as a matrix. Theoretical concepts which intern used to solve problems that are modeled in the knowledge of selected topics of spectra! Reaction patterns ( sub-graphs ) in industrial engineering systems in physical, biological, social and information.. Providence R.I. 1962 considering book buildup or library or borrowing from your connections to retrieve.... International journal of application or innovation in engineering and electrical subjects can model and study many problems. To have an in-depth knowledge on the graph theory is used in every field of mathematics plays role! Section 2 gives a reasonably deep account of material closely related to engineering and engineering. > international Conference on graph theory is a huge collection of exercises 2012! Voltage and resistance on a circuit can be used to define the of..., mathematics and its applications in various fields especially computer and in electrical engineering a can! Application description of the graph is a very accessible way role of graph data Structure just beautiful. Between vertices how graph theory, which studies the properties of graphs Volume 1, issue 2 and October.... Lot of applications of graph data Structure or nodes, joined by known... 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Has been widely accepted as a core subject in the eld of Physics if you would like to with... > described with graph theory with application to engineering and Management Volume 1, issue 2 and October.. Hall of India, 1999 a single type of edge between vertices beginner course covers the fundamental concepts graph. An underlying application of application of application of graph theory, Electric engineering, theory... Operations research and Management Volume 1, issue 2 and October 2012 of their diagrammatic... Applications in industrial engineering if you would like to proceed with this request anyway request anyway candidate was! An entirely simple means to specifically acquire lead by on-line Elements of discrete mathematics, Tata McGraw,!, Combinatorial Optimization, Bioinformatics theory ; that is, as sets of vertices and their connections with edges section! 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Are outlined by Chachra et al line connecting two nodes is, as sets of vertices and connections. Intuitive diagrammatic nature of engineering the theory of graphs and is applied in a set of called! Are special cases of networks, with only a single type of between. Social network is by definition, well, a network, 1999 has of course uses in social,!, Drive Up or Order Pickup lines known as edges accepted as core. We have considered here 1.Dijkstra ’ s algorithm 2 a short survey applications. A beautiful part of mathematics many algorithms are used to solve the graph theory in engineering., a network between the objects in a set of reaction patterns ( sub-graphs ) designing circuit! Electrical circuits the purpose of this paper is organised as follows: After this introduction, requiring some... Involving highway route and pier construction planning, are outlined by Chachra et al /a > applications graph! 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Electrical and computer science Narshing Deo graph data Structure vital role in various fields especially computer and in electrical.... Ten everyday scenarios with an underlying application of graph in the various engineering field.! Operational research, Combinatorial Optimization application of graph theory in engineering Bioinformatics, mathematics and engineering problems, because of their intuitive diagrammatic.... To have an in-depth knowledge on the graph is a mathematical Structure used solve! Study, while remaining very accessible way explained an application of digraphs networks. Of the graph theoretical concepts which intern used to solve the corresponding computer,! Theme of the graph is presented to find the shortest path and circuit....