class+April26

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

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
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.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Deleting any edge in a tree creates a disconnected graph. Adding a new edge to a tree creates a circuit. Example of a tree:
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/20/2012 for the course MATH 103 taught by Professor Berkowitz during the Spring '07 term at Rutgers.

Page1 / 15

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

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online