class+April26

# class+April26 - Math 103, Section 11, Tuesday, April 26,...

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Math 103, Section 11, Tuesday, April 26, 2011 Homework for Chapter 6 will be discussed in class on Tuesday, April 26 and not submitted to Sakai. Exercises (on pages 229-232) 24,26,30,32,40,46 Homework for Chapter 7 will be discussed in class on Tuesday, April 26 and Friday, April 29 Exercises (on pages 266-268) 12,14, 20,24,26 Methods for finding the solution to a Traveling Salesman Problem Method Optimal? Efficient? Brute-force Repetitive nearest- neighbor Cheapest link Chapter 7 The Mathematics of Networks A network is a connected graph. A graph is connected if you can get from any vertex to any other vertex along a path. If there are weights on the edges, it is a weighted network . A network or connected graph with no circuits is called a tree.

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Deleting any edge in a tree creates a disconnected graph. Adding a new edge to a tree creates a circuit. Example of a tree:

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Connect the dots exercise: Start with 8 isolated vertices. Connect the dots (vertices) without forming a circuit. Let M=the number of edges. When M=____, the graph becomes connected. When M=___, the graph will have a circuit. If M=N-1, the network is a tree; if M>N-1, the network has circuits and is not a tree. If a network has N vertices and M edges, then M>=N-1 The difference R=M-(N-1) is the redundancy of the network. In other words, a tree is a network with zero redundancy and a network with positive redundancy is not a tree. Given a connected graph, a
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## This note was uploaded on 01/20/2012 for the course MATH 103 taught by Professor Berkowitz during the Spring '07 term at Rutgers.

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class+April26 - Math 103, Section 11, Tuesday, April 26,...

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