mgf1107lecture16

mgf1107lecture16 - MGF 1107 EXPLORATIONS IN MATHEMATICS...

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MGF 1107 – EXPLORATIONS IN MATHEMATICS LECTURE 16 Hamilton Paths and Hamilton Circuits Before formally defining Hamilton paths and Hamilton circuits, consider the example below. Ex. The following table lists the least expensive one-way fares offered between four cities. Orlando Atlanta Memphis New Orleans Orlando (O) * Atlanta (A) * Memphis (M) * New Orleans (N) * We can create a graph to illustrate this information, letting the vertices represent the cities and listing the airfares on the corresponding edges. It should be noted that the cost of the one-way flight does not depend on the city of origin. So a flight from Orlando to Atlanta costs the same as one from Atlanta to Orlando. This allows us to list the prices on the edges. We call such graphs weighted graphs . The typical problem we look at concerns finding the minimum cost of flying to each of the cities involved before flying back to the original departure point. We call them traveling salesman problems .
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mgf1107lecture16 - MGF 1107 EXPLORATIONS IN MATHEMATICS...

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