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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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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Graphs 1‚ 2‚ 3‚ and 4 show the waveforms for the flute‚ violin‚ piano‚ and oboe. The Fourier Series can be used to explain why each of the instruments have their own unique sound. The flute‚ violin‚ piano and oboe have different combinations of frequencies as each waveform is made of an unique combination of sine and cosine waves‚ and this creates distinct waveforms and allows each instrument to have a unique sound. Recall that the formula of the Fourier Series is f(x)=a_0+∑_(k=1)^∞▒(a_k cos〖πkx/T〗+b_k
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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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WHAT IS A FLANNEL GRAPH. This teaching tool is called by different names: Visual Board Frick Board Slap Board Felt Board Choreograph Videograph The tool consists of only two Parts - a board covered with flannel and objects having fluzzy and napped backing. The principle involved is the interlooking of fibres of two rough or hairy surfaces‚ so that the pieces pressed on to a background which is hard and vertical will stay. It can be illustrated on a larger scale by pressing two
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40 70 Graph: [10 points] Create a graph of your data for this part of the lab. You may use any graphing tool to create the graph‚ but be sure to follow common guidelines for creating a graph. INSERT GRAPH HERE Conclusion: Answer the following questions after completing the lab. 1) Describe the relationship that you observed between pressure and volume in this lab. Refer to your data and/or graph to help support your answer. [5 points] By the information displayed in the graph‚ it shows
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Recognize the difference between grouped and ungrouped data Construct a frequency distribution Construct a histogram‚ a frequency polygon‚ an ogive‚ a pie chart‚ Ungrouped data have not been summarized in any way • are also called raw data • Grouped data • have been organized into a frequency distribution 42 26 32 34 57 30 58 37 50 30 53 40 30 47 49 50 40 32 31 40 52 28 23 35 25 30 36 32 26 50 55 30 58 64 52 49 33 43 46 32 61 31 30 40
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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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The Color Line Essay It was the year 1903 when W.E.B DuBois stated that "the problem of the Twentieth Century is the problem of the color line." The border is the 21st century color line. (Common Dream.org) The color line was basically a line that reserved all the best jobs in the economy for a specific group of individuals. At the same time‚ however‚ these jobs were denied from and kept away from another group of people (Common Dream.org) This was done so through both private institutions and
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routine that the father worked while the mother stayed home to care for the children and the household. In this era‚ there are some extenuating circumstances where parents cannot totally commit to monitoring their children. They may be forced into single parenting‚ they may be required to work more than one job‚ or they may have too many children which would render them unable to properly supervise the child that needs the most supervision. On some occasions‚ these unsupervised adolescents may turn
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