Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 14 - Graph Theory - 14.1 Graphs, Paths, and Circuits - Exercise Set 14.1: 1

Answer

Pittsburgh has 6 games during the week. Pittsburgh plays the following teams: St. Louis, Chicago, Philadelphia, Montreal Pittsburgh plays St. Louis once. Pittsburgh plays Chicago once. Pittsburgh plays Philadelphia twice. Pittsburgh plays Montreal twice.

Work Step by Step

The vertex for Pittsburgh has 6 edges connected to it, so Pittsburgh has 6 games during the week. If an edge connects the vertex for Pittsburgh to the vertex for another team, then Pittsburgh plays that team. Pittsburgh plays the following teams: St. Louis, Chicago, Philadelphia, Montreal The number of edges connecting the vertex for Pittsburgh to the vertex for another team shows how many times Pittsburgh plays that team. Pittsburgh plays St. Louis once. Pittsburgh plays Chicago once. Pittsburgh plays Philadelphia twice. Pittsburgh plays Montreal twice.
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