Ch 7 Notes

# Ch 7 Notes - Chapter 7 Fredonia State wants to build an...

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Chapter 7

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Fredonia State wants to build an underground walkway to make it easier for students to get to their destinations especially on those cold, rainy or snowy days. The goal is to come up with a system that would allow students to walk underground to each site, but would require the fewest number of yards to construct. Fenton Steele Campus Center Thompson Library Less construction, less \$\$
T F C L S After doing some research, the college grounds crew created the following diagram depicting possible tunnel routes. The number of yards between each of the buildings is illustrated on the graph. Can you find a way to construct the tunnels so that it is possible for students to walk underground to each of these buildings? 53 68 75 126 88 71 81 102 64

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Examining Some Possibilities How many yards of tunnel will need to be constructed under this possibility? Can you see any way that the grounds crew could lessen the number of yards? T F C L S 53 68 75 88 81 64 429
If the grounds crew takes out some redundant edges, they could reduce the total yardage. By eliminating the tunnel from T to F, they could save 75 yards Likewise, by eliminating the tunnel from S to C, they could save 81 yards Hey, with fewer tunnels needed to be constructed, maybe your tuition costs will be lowered! New Total Yardage: T F C L S 53 68 75 88 81 64 A savings of 156 yards! 273

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Network: another name for a connected graph Tree: a network with no circuits (a sequence of adjacent edges that begin and end at the same vertex, each edge used only once) YES Is it a TREE? NO YES YES
Spanning Tree: a subgraph that connects all of the vertices of the network and has no circuits edges must come from the original graph Spanning Trees of a graph with N vertices must have N – 1

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## This note was uploaded on 05/06/2008 for the course MATH 110 taught by Professor Pietro during the Spring '08 term at SUNY Fredonia.

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Ch 7 Notes - Chapter 7 Fredonia State wants to build an...

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