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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Polar Bear Crisis In May 2008‚ the U.S listed the polar bear as a threatened species under the Endangered Species Act. The Arctic is one of the most discussed on climate change‚ due to the fact that warming is greatest there and because what happens in the Arctic has the can eventually impact the rest of the Earth. So far‚ not only has it affected the way the ice is melting and the weather is changing‚ but it is mainly affecting the animals that are living there (for example‚ polar bears). Although
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07 Polar Bears I. Introduction a. Polar bears have lived in extremely harsh conditions‚ and with global warming made their way to being endangered. Polar bears have opened eyes on how we see extreme weather and how to survive in it. i. Body of bear‚ what they eat‚ where they find shelter II. Body of polar bear a
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a different species. Polar bears have gone under a series of evolutionary changes over time to help them survive in conditions on the planet some such adaptations include larger paws‚ thicker white fur‚ extra fat to keep them warm and more recently they have developed polar bear type teeth. These
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There are four types of evolution‚ those being adaptive‚ convergent‚ divergent‚ and co-evolution. Divergent evolution is when two or more animals originate from a common genetic base. To prove divergent evolution in animals‚ the Ursus Maritimus or polar bear is an example. Divergent evolution is when similar animals branch off becoming dissimilar as time goes. Divergent evolution occurred 125‚000 years ago when brown bears were isolated from their ancestors. This movement got them stranded and
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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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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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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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The Polar Bear and Adaptations The polar bear is seen by many as the beautiful white bear that lives in the cold and ice of the areas within the North Pole. They may never look beyond the beauty to see the animal has progressed through natural selection to become a creature that endures and thrives in the frigid temperatures and prolific ice. The polar bear has adapted in various ways such as temperature regulation‚ hunting skills‚ movement in water and on ice. The bears white coat makes hunting
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