Excursions in Modern Mathematics (9th Edition)
9th Edition
ISBN: 9780134468372
Author: Peter Tannenbaum
Publisher: PEARSON
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Textbook Question
Chapter 7, Problem 7E
Consider the network shown in.
a. In addition to the pair
b. If you can, find two vertices in the network having seven degrees of separation between them. If you can’t, then briefly explain why you don’t think there are any.
c. What is the diameter of the network?
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Let ∆ABC have vertices at A = (0,0), B = (3,4), and C = (12,5). Let ∆HFK have vertices at H = (6,0), F = (8,1.5), and K = (12,2.5). Is ∆ABC similar to ∆HFK ?
Which similarity theorem would you use to check whether ∆ABC and ∆HFK are similar?
Determine whether ∆ABC and ∆HFK are similar.
Which of the graphs below have Euler circuits?
1) II only 2) I only 3) neither I nor II 4) both I and II
Which of the graphs below have Euler circuits?
1) I only 2) II only 3) both I and II 4) neither I nor II
Chapter 7 Solutions
Excursions in Modern Mathematics (9th Edition)
Ch. 7 - A computer lab has seven computers labeled A...Ch. 7 - The following is a list of the electrical power...Ch. 7 - Consider the network shown in Fig.720_. a. How...Ch. 7 - Consider the network shown in Fig.721_. a. How...Ch. 7 - Consider once again the network shown in. Fig720_....Ch. 7 - Consider once again the network shown in. Fig721_....Ch. 7 - Consider the network shown in. Fig722. This is the...Ch. 7 - Consider the network shown in. Fig723_. This is...Ch. 7 - Consider the tree shown in. Fig724_. a. How many...Ch. 7 - Consider the tree shown in. Fig725. a. How many...
Ch. 7 - In Exercises 11 through 24 you are given...Ch. 7 - Prob. 12ECh. 7 - Prob. 13ECh. 7 - Prob. 14ECh. 7 - In Exercises 11 through 24 you are given...Ch. 7 - Prob. 16ECh. 7 - Prob. 17ECh. 7 - Prob. 18ECh. 7 - Prob. 19ECh. 7 - In Exercises 11 through 24 you are given...Ch. 7 - Prob. 21ECh. 7 - Prob. 22ECh. 7 - Prob. 23ECh. 7 - Prob. 24ECh. 7 - Prob. 25ECh. 7 - Consider the network shown in Fig.727_. a. Find a...Ch. 7 - Prob. 27ECh. 7 - Consider the network shown in Fig.729_. a. Find a...Ch. 7 - Prob. 29ECh. 7 - Prob. 30ECh. 7 - Prob. 31ECh. 7 - Prob. 32ECh. 7 - Prob. 33ECh. 7 - Prob. 34ECh. 7 - Prob. 35ECh. 7 - The 4 by 5 grid shown in Fig. 7-37 represents a...Ch. 7 - Prob. 37ECh. 7 - Find the MST of the network shown in Fig. 7-39...Ch. 7 - Find the MST of the network shown in Fig. 7-40...Ch. 7 - Find the MST of the network shown in Fig. 7-41...Ch. 7 - Prob. 41ECh. 7 - Find the MaxST of the network shown in Fig. 7-39...Ch. 7 - Find the MaxST of the network shown in Fig. 7-40...Ch. 7 - Prob. 44ECh. 7 - The mileage chart in Fig. 742 shows the distances...Ch. 7 - Figure 7-43a shows a network of roads connecting...Ch. 7 - Prob. 47ECh. 7 - Prob. 48ECh. 7 - Prob. 49ECh. 7 - This exercise refers to weighted networks where...Ch. 7 - Prob. 51ECh. 7 - Prob. 52ECh. 7 - Prob. 53ECh. 7 - Prob. 54ECh. 7 - Prob. 55ECh. 7 - Prob. 56ECh. 7 - A bipartite graph is a graph with the property...Ch. 7 - Prob. 58ECh. 7 - Prob. 59E
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- (a) Which vertices can reach vertex 2 by a walk of length 3? (d) Is (2, 2) in the transitive closure of G? (e) Is (5, 3) an edge in G3? (f) Is there a closed walk of length 3 in G?arrow_forwardS= {A,D} and T={B,C,E} for the network in exercise #8 Tell whether the given sets of S, T form a cut for the network indicated. If so, give the capacity of the cut. If not, tell why.arrow_forwardDraw the network diagram for the above project.arrow_forward
- Prove that If a connected planar simple graph has e edges and v vertices with v ≥ 3 and no circuits of length three, then e ≤ 2v − 4. (Show work)arrow_forward(a) What are the edges incident on v2? (b) What are the vertices adjacent to v2 ? (c) What are the edges adjacent to e2 ?arrow_forwardFor which values of m and n does the complete bipartite graph Km,n have an Euler circuit?arrow_forward
- Consider the following graph, which represents the one-way airfare between five cities. A B C D E A * $220 $240 $290 $430 B $220 * $260 $320 $360 C $240 $260 * $180 $300 D $290 $320 $180 * $250 E $430 $360 $300 $250 * Graph the following to represent the information in the table. Use vertices to represent the cities and weights on appropriate edges to show the airfares. Next, assume that you are a salesman who lives in one of the cities (pick any city except for A) and required to fly to all four of the other cities and return to your home city. Describe how you would use the Nearest Neighbor Method to determine the optimal route. What is the total cost for this Hamilton circuit?arrow_forwardLet x and y be two adjacent vertices in the complete bipartite graph Kn,n, n ≥ 3.Find the number of x-y paths of length 2, of length 3, and of length 4.arrow_forwardFor which m and n does the graph Km,n contain an Euler path? An Euler circuit? Explain.arrow_forward
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