Applications of Graph Theory in Real Life Sharathkumar.A‚ Final year‚ Dept of CSE‚ Anna University‚ Villupuram Email: kingsharath92@gmail.com Ph. No: 9789045956 Abstract Graph theory is becoming increasingly significant as it is applied to other areas of mathematics‚ science and technology. It is being actively used in fields as varied as biochemistry (genomics)‚ electrical engineering (communication networks and coding theory)‚ computer science (algorithms and computation) and operations
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Graph theory - the study of graphs and networks‚ is often considered part of combinatorics‚ but has grown large enough and distinct enough‚ with its own kind of problems‚ to be regarded as a subject in its own right.[12] Graphs are one of the prime objects of study in discrete mathematics. They are among the most ubiquitous models of both natural and human-made structures. They can model many types of relations and process dynamics in physical‚ biological and social systems. In computer science‚
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V. Adamchik 1 Graph Theory Victor Adamchik Fall of 2005 Plan 1. Basic Vocabulary 2. Regular graph 3. Connectivity 4. Representing Graphs Introduction A.Aho and J.Ulman acknowledge that “Fundamentally‚ computer science is a science of abstraction.” Computer scientists must create abstractions of real-world problems that can be represented and manipulated in a computer. Sometimes the process of abstraction is simple. For example‚ we use a logic to design a computer circuits. Another example - scheduling
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Trenerry §5 Graph Theory Loosely speaking‚ a graph is a set of dots and dot-connecting lines. The dots are called vertices and the lines are called edges. Formally‚ a (finite) graph G consists of A finite set V whose elements are called the vertices of G; A finite set E whose elements are called the edges of G; A function that assigns to each edge e ∈ E an unordered pair of vertices called the endpoints of e. This function is called the edge-endpoint function. Note that these graphs are not related
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Tree definitions If you already know what a binary tree is‚ but not a general tree‚ then pay close attention‚ because binary trees are not just the special case of general trees with degree two. I use the definition of a tree from the textbook‚ but bear in mind that other definitions are possible. Definition. A tree consists of a (possible empty) set of nodes. If it is not empty‚ it consists of a distinguished node r called the root and zero or more non-empty subtrees T1‚ T2‚ …‚ Tk such that there
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Graphs 1 Introduction We have studied one non-linear data structure so far i.e Trees. A graph is another non-linear data structure that is widely used to solve many real-life computing problems. For example‚ we need to use a graph to find out whether two places on a road-map are connected and what is the shortest distance between them. Graphs are used in simulating electrical circuits to find out current flows and voltage drops at various points in the circuit. Graphs are widely used in telephone
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Introduction in Graph Theory (BASIC CONCEPTS) BASIC CONCEPTS We used decision trees in Unit DT and used them to study decision making. However‚ we did not look at their structure as trees. In fact‚ we didn’t even define a tree precisely. What is a tree? It is a particular type of graph‚ which brings us to the subject of this unit. What is a Graph? There are various types of graphs‚ each with its own definition. Unfortunately‚ some people apply the term “graph” rather loosely‚ so
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How many optimal solutions are there for a given problem ? - 4- Combinatorial Optimization (C.O.) problems Different fields in Optimization: Linear Programming Non-Linear Optimization Integer – Mixed Linear Programming Graph / network optimization Routing‚ Scheduling‚ Supply Chain‚… Combinatorial optimization studies optimization on finite and discrete domains. Find the minimum s* of f on a finite set S. f ( s ) Min f ( s) sS - 5- Characteristics
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treated all complex networks as being completely random. This theory had its roots in the work of two mathematicians‚ Paul Erdos and Alfred Renyi. Their work suggested that systems such as communications could be effectively modelled by connecting nodes with randomly placed links. Their simple approach revitalised graph theory and led to the emergence of the field of random networks. An important prediction of random network theory is regardless of the random placement of links most nodes will
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Graphs are often used to deliver a visual and compelling case in many applications and businesses. Graphs are the information delivery vehicle of choice for many numerical data applications. With graphs a lot of information can be condensed into a visually descriptive object. They reduce the amount of time that would have been expended in reading or parsing through a lot of information. On the other hand‚ they can also be easily used to misrepresent or skew interpretation towards a favorable
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