Login Registrieren

Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Discrete Mathematics and its Applications

Kenneth H. Rosen

$Math Studyset Vaia Explanations$ Math

7th Edition · 808 pages

ISBN: 9780073383095

Chapter 10: Q17E (page 717)

To determine the paths with the minimum toll between Newark and Camden and between Newark and Cape May.

Short Answer

Expert verified

The path with minimum toll between Newark and Camden is through Woodbridge.

The path with minimum toll between Newark and Cape May is through Woodbridge and Camden.

Step by step solution

01

Given data

The graph representing the tolls between the cities.

02

Concept used of Dijkstra’s algorithm

Dijkstra's algorithm allows us to find the shortest path between any two vertices of a graph.

03

Find the least path

Any path exiting Newark must pass through Woodbridge. The direct path from Woodbridge to Camden has zero toll \((\$ 0.00)\). Thus, the path with the least toll from Newark to Camden is through Woodbridge. The same consideration (as the tolls between Woodbridge and Camden, and Camden and Cape May are zero \((\$ 0.00))\) shows that the path with the least toll between Newark and Cape May is through Woodbridge and Camden.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

State the four-color theorem. Are there graphs that cannot be colored with four colors?

Determine whether the following graphs are self-converse.

a)

b)

a) Describe three different methods that can be used torepresent a graph.

b) Draw a simple graph with at least five vertices andeight edges. Illustrate how it can be represented using the methods you described in part (a).

Solve the art gallery problem by proving the art gallery theorem, which states that at most (n/3) guards are needed to guard the interior and boundary of a simple polygon with n vertices.

(Hint: Use Theorem 1 in Section 5.2 to triangulate the simple polygon into n - 2 triangles. Then show that it is possible to color the vertices of the triangulated polygon using three colors so that no two adjacent vertices have the same color. Use induction and Exercise 23 in Section 5.2. Finally, put guards at all vertices that are colored red, where red is the color used least in the coloring of the vertices. Show that placing guards at these points is all that is needed.)

The mathematics department has six committees, each

meeting once a month. How many different meeting times

must be used to ensure that no member is scheduled to

attend two meetings at the same time if the committees

are,

\(\begin{array}{*{20}{l}}\begin{array}{l}{C_1} = \{ \;Arlinghaus, Brand, Zaslavsky\;\} ,\\{C_2} = \{ \;Brand, Lee, Rosen\;\} ,\end{array}\\\begin{array}{l}{C_3} = \{ \;Arlinghaus, Rosen, Zaslavsky\;\} ,\\{C_4} = \{ \;Lee, Rosen, Zaslavsky\;\} ,\end{array}\\\begin{array}{l}{C_5} = \{ \;Arlinghaus, Brand\;\} ,\\{C_6} = \{ \;Brand, Rosen, Zaslavsky\;\} \end{array}\end{array}\)

See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free