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Unformatted text preview: 11COMP170Discrete Mathematical Toolsfor Computer ScienceDiscrete Math for Computer ScienceK. Bogart, C. Stein and R.L. DrysdaleSection 6.1, pp. 309320Intro to GraphsVersion 2.0: Last updated, May 13, 2007Slidesc2005 by M. J. Golin and G. Trippen21Graphs•The Degree of a Vertex•Connectivity•Cycles•Trees•Basic Definitions31Graphs32GraphsFundamental topic in discrete math and CS.33GraphsFundamental topic in discrete math and CS.Important because it’s used tomodel many commonsituationsand to naturally describe many algorithms.34GraphsFundamental topic in discrete math and CS.Important because it’s used tomodel many commonsituationsand to naturally describe many algorithms.Example35GraphsFundamental 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.36GraphsFundamental 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.4142What is theminimumnumberof links needed to send amessage fromBtoNO?43What is theminimumnumberof links needed to send amessage fromBtoNO?44What is theminimumnumberof links needed to send amessage fromBtoNO?3:B – CH – ME – NO.45What is theminimumnumberof links needed to send amessage fromBtoNO?3:B – CH – ME – NO.Which city/cities has/have themost communication links emanating from it/them?46What is theminimumnumberof links needed to send amessage fromBtoNO?3:B – CH – ME – NO.Which city/cities has/have themost communication links emanating from it/them?47What is theminimumnumberof links needed to send amessage fromBtoNO?3:B – CH – ME – NO.Which city/cities has/have themost communication links emanating from it/them?A:6links.48What is theminimumnumberof links needed to send amessage fromBtoNO?3:B – CH – ME – NO.Which city/cities has/have themost communication links emanating from it/them?A:6links.What is the total number ofcommunication links?49What is theminimumnumberof links needed to send amessage fromBtoNO?3:B – CH – ME – NO.Which city/cities has/have themost communication links emanating from it/them?A:6links.What is the total number ofcommunication links?20links.51GraphG52consists of a set ofverticesV,V=n,GraphG53consists of a set ofverticesV,V=n,and a set ofedgesE,E=m.GraphG54consists of a set ofverticesV,V=n,and a set ofedgesE,E=m.Each edge has twoendpoints.GraphG55consists of a set ofverticesV,V=n,and a set ofedgesE,E=m.Each edge has twoendpoints....
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 Spring '10
 M.J.Golin
 Computer Science

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