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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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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Graphs and Function What is the relation between the graphs and function and how was it applied in the real world? Graphs are frequently used in national magazines and newspaper to present information about things such as the world’s busiest airports (O’Hare in China is first‚ Heathrow in London is sixth)‚ about the advertising-dollar receivers in the United States (newspaper are first‚ radio is fourth) and about NCAA men’s golf team title winner (Yael is first‚ Houston is second). The
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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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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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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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Trees and Graphs Pat Hanrahan Tree Drawing Page 1 Why Trees? Hierarchies File systems and web sites Organization charts Categorical classifications Similiarity and clustering Branching processes Genealogy and lineages Phylogenetic trees Decision processes Indices or search trees Decision trees Tournaments Two Major Visual Representations Connection: Node / Link Diagrams Containment / Enclosure F6 G6 H6 J36 U8 B10 C30 L7 M7 V12 O4 P4 Q4 R4 S4 T4 W8 Page
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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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Find an example online of a graph used in real-life (include the link that goes directly to the webpage with the graph). Describe at least one mathematical feature of the graph (e.g. shape‚ slope‚ coordinates‚ axes‚ quadrants‚ etc.) and how the feature/graph can help us to analyze the real-life situation. Graph for Health Care Spending http://www.kff.org/insurance/snapshot/OECD042111.cfm In this link‚ there are several graphs from various perspectives regarding Health Care Spending in the United
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Graphs - Introduction Terminology Graph ADT Data Structures Reading: 12.1-12.2 COSC 2011‚ Summer 2004 Definition • A graph is a pair (V‚ E)‚ where – V is a set of nodes‚ called vertices – E is a collection of pairs of vertices‚ called edges • Both are objects (i.e. store data) G E B F A Vertex city computer web page airport C D COSC 2011‚ Summer 2004 H Edge road cable hyperlink flight Example Applications • • • • • Electronic circuits – Printed circuit board – Integrated circuit Transportation
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