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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Conics are surprisingly easy! There are four types of conic sections‚ circles‚ parabolas‚ ellipses‚ and hyperbolas. The first type of conic‚ and easiest to spot and solve‚ is the circle. The standard form for the circle is (x-h)^2 + (y-k)^2 = r^2. The x-axis and y-axis radius are the same‚ which makes sense because it is a circle‚ and from In order to graph an ellipse in standard form‚ the center is first plotted (the (h‚ k)). Then‚ the x-radius is plotted on both sides of the center‚ and the y-radius
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Graphs‚ Groups and Surfaces 1 Introduction In this paper‚ we will discuss the interactions among graphs‚ groups and surfaces. For any given graph‚ we know that there is an automorphism group associated with it. On the other hand‚ for any group‚ we could associate with it a graph representation‚ namely a Cayley graph of presentations of the group. We will first describe such a correspondence. Also‚ a graph is always embeddable in some surface. So we will then focus on properties of graphs
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1.2 Basics of Functions and Their Graphs Introduction to Relations Domain and Range of a Relation Any set of ordered pairs (x‚y) is called a relation in x and y. Furthermore‚ The set of first components in the ordered pairs is called the domain of the relation. The set of second components in the ordered pairs is called the range of the relation. Definition of Function and Vertical Line Test Definition of a Function Given a relation in x and y‚ we say “y is a function of x” if for every
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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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------------------------------------------------- ------------------------------------------------- Speed Speed is defined as a measure of the distance an object travels in a given length of time. The average speed of an object can be determined from the equation below: Thus‚ if a car travels 100 meters in 5 seconds its average speed can be calculated as; Average speed = 100/5 = 20 meters per second Average speed is used to give the speed of an object over a given interval of time‚ if
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Sabrina Lebron December 2‚ 2010 Professor Ann Impens Week 1 Assignment The chart of graph selected comes from the US Centers for Disease Control and Preventions MMWR in the article‚ "Heat Illness Among High School Athletes --- United States‚ 2005--2009" http://www.cdc.gov/mmwr/preview/mmwrhtml/mm5932a1.htm?s_cid=mm5932a1_w Identify the type of chart or graph and what this type of chart or graph usually depicts. At the bottom of the article‚ there is a verticle bar chart of the Number
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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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Distance Time Graphs Definitions * Speed: Speed is a scalar quantity that refers to "how fast an object is moving." Speed can be thought of as the rate at which an object covers distance. A fast-moving object has a high speed and covers a relatively large distance in a short amount of time. * Velocity: Velocity is a vector quantity that refers to "the rate at which an object changes its position." When evaluating the velocity of an object‚ one must keep track of direction. It would not
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The usage of graphs are essential in the illustration and comprehension of statistical output. They type of graphs used depends on the author and the view they are trying to portrait. Graphs can be used to prove or disprove a theory based on its presentation. The Following graph is used as a visually depiction of a sample of grade school childern of whom an IQ exam was performed. Figure: The histogram figures shown are extracts of an IQ test performed on elementary school subjects and
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