Excursions In Modern Mathematics, 9th Edition
9th Edition
ISBN: 9780134494142
Author: Tannenbaum
Publisher: PEARSON
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Chapter 8, Problem 18E
The digraph in Fig. 8-29 is an example of a tournament digraph. In this example the vertices of the digraph represent five volleyball teams in a round-robin tournament (i.e., every team plays every other team). An arc XY represents that X defeated Y in the tournament. (Note: There are no ties in volleyball.)
a. Which team won the tournament? Explain.
b. Which team came in last in the tournament? Explain.
c. Suppose that you are given the tournament digraph of some tournament. What does the indegree of a vertex represent? What does the outdegree of a vertex represent?
d. If T denotes the tournament digraph for a round-robin tournament with N teams, then for any vertex X in T, the indegree of X plus the outdegree of X = N — 1. Explain why.
Figure 8-29
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Chapter 8 Solutions
Excursions In Modern Mathematics, 9th Edition
Ch. 8 - For the digraph shown in Fig. 8-25, find a.the...Ch. 8 - For the digraph shown in Fig. 8-26, find Figure...Ch. 8 - For the digraph in Fig. 8-25, find a.all path of...Ch. 8 - For the digraph in Fig. 8-26, find a.a path of...Ch. 8 - For the digraph in Fig. 8-25, find a.all cycles of...Ch. 8 - For the digraph in Fig. 8-26, find a.all cycles of...Ch. 8 - Prob. 7ECh. 8 - For the digraph in Fig.8-26, find a.all vertices...Ch. 8 - a.Draw a digraph with vertex-set V={A,B,C,D} and...Ch. 8 - a.Draw a digraph with vertex-set V={A,B,C,D} and...
Ch. 8 - Prob. 11ECh. 8 - Consider the digraph with vertex-set V={V,W,X,Y,Z}...Ch. 8 - Prob. 13ECh. 8 - Prob. 14ECh. 8 - Prob. 15ECh. 8 - A mathematics textbook consists of 10 chapters....Ch. 8 - Prob. 17ECh. 8 - The digraph in Fig. 8-29 is an example of a...Ch. 8 - Prob. 19ECh. 8 - Wobble, a start-up company, is developing a search...Ch. 8 - A project consists of eight tasks labeled A...Ch. 8 - A project consists of eight tasks labeled A...Ch. 8 - Prob. 23ECh. 8 - Prob. 24ECh. 8 - Prob. 25ECh. 8 - A ballroom is to be set up for a large wedding...Ch. 8 - Prob. 27ECh. 8 - Prob. 28ECh. 8 - Exercises 29 through 32 refer to a project...Ch. 8 - Exercises 29 through 32 refer to a project...Ch. 8 - Prob. 31ECh. 8 - Exercises 29 through 32 refer to a project...Ch. 8 - Prob. 33ECh. 8 - Exercises33 and 34 refer to the Martian Habitat...Ch. 8 - Prob. 35ECh. 8 - Prob. 36ECh. 8 - Prob. 37ECh. 8 - Using the priority list G,F,E,D,C,B,A, schedule...Ch. 8 - Prob. 39ECh. 8 - Using the priority list G,F,E,D,C,B,A, schedule...Ch. 8 - Prob. 41ECh. 8 - Prob. 42ECh. 8 - Prob. 43ECh. 8 - Use the decreasing-time algorithm to schedule the...Ch. 8 - Prob. 45ECh. 8 - Use the decreasing-time algorithm to schedule the...Ch. 8 - Prob. 47ECh. 8 - Consider the project described by the digraph...Ch. 8 - Consider the project described by the digraph...Ch. 8 - Consider the project described by the digraph...Ch. 8 - Consider the project digraph shown in Fig.8-40....Ch. 8 - Consider the project digraph shown in Fig.8-40....Ch. 8 - Prob. 53ECh. 8 - Consider the project digraph shown in Fig.8-41....Ch. 8 - Schedule the Apartments Unlimited project given in...Ch. 8 - Schedule the project given in Exercise26 Table8-5...Ch. 8 - Consider the project described by the project...Ch. 8 - Consider the project digraph shown in Fig.8-43,...Ch. 8 - Prob. 59ECh. 8 - Symmetric and totally asymmetric digraphs. A...Ch. 8 - Prob. 61ECh. 8 - Let W represent the sum of the processing times of...Ch. 8 - You have N=2 processors to process M independent...Ch. 8 - You have N=3 processors to process M independent...Ch. 8 - You have N=2 processor to process M+1 independent...
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