L19_IntroGraphs

L19_IntroGraphs - 1-1COMP170Discrete Mathematical Toolsfor...

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Unformatted text preview: 1-1COMP170Discrete Mathematical Toolsfor Computer ScienceDiscrete Math for Computer ScienceK. Bogart, C. Stein and R.L. DrysdaleSection 6.1, pp. 309-320Intro to GraphsVersion 2.0: Last updated, May 13, 2007Slidesc2005 by M. J. Golin and G. Trippen2-1Graphs•The Degree of a Vertex•Connectivity•Cycles•Trees•Basic Definitions3-1Graphs3-2GraphsFundamental topic in discrete math and CS.3-3GraphsFundamental topic in discrete math and CS.Important because it’s used tomodel many commonsituationsand to naturally describe many algorithms.3-4GraphsFundamental topic in discrete math and CS.Important because it’s used tomodel many commonsituationsand to naturally describe many algorithms.Example3-5GraphsFundamental topic in discrete math and CS.Important because it’s used tomodel many commonsituationsand to naturally describe many algorithms.ExampleMap of some cities in eastern US.3-6GraphsFundamental topic in discrete math and CS.Important because it’s used tomodel many commonsituationsand to naturally describe many algorithms.ExampleMap of some cities in eastern US.with communication lines existingbetween certain pairs of these cities.4-14-2What is theminimumnumberof links needed to send amessage fromBtoNO?4-3What is theminimumnumberof links needed to send amessage fromBtoNO?4-4What is theminimumnumberof links needed to send amessage fromBtoNO?3:B – CH – ME – NO.4-5What is theminimumnumberof links needed to send amessage fromBtoNO?3:B – CH – ME – NO.Which city/cities has/have themost communication links em-anating from it/them?4-6What is theminimumnumberof links needed to send amessage fromBtoNO?3:B – CH – ME – NO.Which city/cities has/have themost communication links em-anating from it/them?4-7What is theminimumnumberof links needed to send amessage fromBtoNO?3:B – CH – ME – NO.Which city/cities has/have themost communication links em-anating from it/them?A:6links.4-8What is theminimumnumberof links needed to send amessage fromBtoNO?3:B – CH – ME – NO.Which city/cities has/have themost communication links em-anating from it/them?A:6links.What is the total number ofcommunication links?4-9What is theminimumnumberof links needed to send amessage fromBtoNO?3:B – CH – ME – NO.Which city/cities has/have themost communication links em-anating from it/them?A:6links.What is the total number ofcommunication links?20links.5-1GraphG5-2consists of a set ofverticesV,|V|=n,GraphG5-3consists of a set ofverticesV,|V|=n,and a set ofedgesE,|E|=m.GraphG5-4consists of a set ofverticesV,|V|=n,and a set ofedgesE,|E|=m.Each edge has twoendpoints.GraphG5-5consists of a set ofverticesV,|V|=n,and a set ofedgesE,|E|=m.Each edge has twoendpoints....
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L19_IntroGraphs - 1-1COMP170Discrete Mathematical Toolsfor...

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