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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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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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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and amortization policies may differ from company to company. EBITDA‚ PBT & PAT EBITDA is an acronym for Earnings Before Interest‚ Taxes‚ Depreciation‚ and Amortization. PBT stands for Profit Before Tax‚ and PAT stands for Profit After Tax. The graph visually shows how the net profit of the company stand reduced due to the impact of Interest‚ Depreciation‚ and Tax. Total Assets & Asset Turnover Ratio Total Assets is the sum of all assets‚ current and fixed. The asset turnover ratio measures
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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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Practice Name ___RaeAnne Phillips________________________________ Date __________ ▪ Save this file as a WORD document with a new name (LastNameGraph1) ▪ Use Create a Graph (http://nces.ed.gov/nceskids/graphing/) to graph the following data sets. ▪ Copy and paste the graphs AFTER each data set. ▪ Answer the questions AFTER each graph. ▪ Save Frequently! ▪ Email me (mruthenberg@findlaycityschools.org) the finished document. 1. Baby chickens‚ like all baby birds‚ require a constant source of
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Essential Graphs for Microeconomics Basic Economic Concepts ( Production Possibilities Curve Nature & Functions of Product Markets ( Demand and Supply: Market clearing equilibrium (Floors and Ceilings (Consumer and Producer Surplus (Effect of Taxes Theory of the Firm (Short Run Cost (Long Run Cost
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| | | | | 420 | | | | | 450 | | | | | 480 | | | | | 510 | | | | | 540 | | | | | 570 | | | | | 600 | | | | | 630 | | | | | 660 | | | | | Make two graphs of your data. On one graph plot the data from the pure water. On the other graph plot the data from the salt solution. On both plot temperature on the y-axis and time on the x-axis. B. Record the freezing point of the pure water and the freezing point of the salt solution. Freezing
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The Line The "line" that the film’s title refers to is the poverty line‚ or the line between "the haves and have-nots‚" as one person in the film put it. The documentary highlights the stories of four people who have found themselves on both sides of the line: a former bank vice president who lost his job‚ a Louisiana fisherman whose livelihood is threatened by environmental degradation and hurricanes‚ a former homeless man‚ and a woman that grew up in a high crime neighborhood‚ lifted herself
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According to the results‚ there was no significant difference between the filtered 100% water composition‚ and the filtered 90% water 10% soap composition. However‚ based on fFigure 2‚ the Average of Absorbance graph‚ showed that growth of the algae for the 100% water composition was observed to be slightly higher than the 90% water 10% soap composition. Meaning the soap may have slightly affected the growth of the algae‚ in some way. One possible‚ reason for a slightly higher growth for the filtered
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