Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)
3rd Edition
ISBN: 9780134689555
Author: Edgar Goodaire, Michael Parmenter
Publisher: PEARSON
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Concept explainers

Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …
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Chapter 13.1, Problem 22E

  1. [BB] suppose G is a connected planar graph in which every vertex has degree at least 3. Prove that at least two regions of G have at most five edges on their boundaries.

  2. Establish (a) for planar graphs that are not connected.

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Chapter 13 Solutions

Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)

Ch. 13.1 - Prob. 1TFQCh. 13.1 - Prob. 2TFQCh. 13.1 - Prob. 3TFQCh. 13.1 - Prob. 4TFQCh. 13.1 - Prob. 5TFQCh. 13.1 - Prob. 6TFQCh. 13.1 - Prob. 7TFQCh. 13.1 - Prob. 8TFQCh. 13.1 - Prob. 9TFQCh. 13.1 - Prob. 10TFQ
Ch. 13.1 - [BB] Show that the graph is planar by drawing an...Ch. 13.1 - Prob. 2ECh. 13.1 - Prob. 3ECh. 13.1 - 4. One of the two graphs is planar; the other is...Ch. 13.1 - Prob. 5ECh. 13.1 - Prob. 6ECh. 13.1 - Prob. 7ECh. 13.1 - Prob. 8ECh. 13.1 - Prob. 9ECh. 13.1 - Prob. 10ECh. 13.1 - Prob. 11ECh. 13.1 - Prob. 12ECh. 13.1 - Prob. 13ECh. 13.1 - Prob. 14ECh. 13.1 - Prob. 15ECh. 13.1 - Discover what you can about Kazimierz Kuratowski...Ch. 13.1 - Prob. 17ECh. 13.1 - Prob. 18ECh. 13.1 - Prob. 19ECh. 13.1 - [BB] Prove that every planar graph V2 vertices has...Ch. 13.1 - Prob. 21ECh. 13.1 - [BB] suppose G is a connected planar graph in...Ch. 13.1 - Prob. 23ECh. 13.1 - Prob. 24ECh. 13.1 - Prob. 25ECh. 13.2 - Prob. 1TFQCh. 13.2 - Prob. 2TFQCh. 13.2 - Prob. 3TFQCh. 13.2 - Prob. 4TFQCh. 13.2 - Prob. 5TFQCh. 13.2 - Prob. 6TFQCh. 13.2 - Prob. 7TFQCh. 13.2 - Prob. 8TFQCh. 13.2 - Prob. 9TFQCh. 13.2 - Prob. 10TFQCh. 13.2 - Prob. 1ECh. 13.2 - Prob. 2ECh. 13.2 - Prob. 3ECh. 13.2 - Prob. 4ECh. 13.2 - Prob. 5ECh. 13.2 - Prob. 6ECh. 13.2 - Prob. 7ECh. 13.2 - Prob. 8ECh. 13.2 - Prob. 9ECh. 13.2 - Prob. 10ECh. 13.2 - Prob. 11ECh. 13.2 - Prob. 12ECh. 13.2 - Prob. 13ECh. 13.2 - Prob. 14ECh. 13.2 - Prob. 15ECh. 13.2 - Prob. 16ECh. 13.2 - Prob. 17ECh. 13.2 - Prob. 18ECh. 13.2 - Prob. 19ECh. 13.2 - Prob. 20ECh. 13.2 - [BB] The following semester, all the students in...Ch. 13.2 - Prob. 22ECh. 13.2 - 23. The local day care center has a problem...Ch. 13.2 - Prob. 24ECh. 13.2 - Prob. 25ECh. 13.2 - (a) [BB] Draw the dual graph of the cube...Ch. 13.2 - [BB] is it possible for a plane graph, considered...Ch. 13.3 - Prob. 1TFQCh. 13.3 - Prob. 2TFQCh. 13.3 - Prob. 3TFQCh. 13.3 - Prob. 4TFQCh. 13.3 - Prob. 5TFQCh. 13.3 - Prob. 6TFQCh. 13.3 - Prob. 7TFQCh. 13.3 - Prob. 8TFQCh. 13.3 - Prob. 9TFQCh. 13.3 - Prob. 10TFQCh. 13.3 - Prob. 1ECh. 13.3 - Prob. 2ECh. 13.3 - [BB] True or False? A line-of-sight graph is...Ch. 13.3 - Prob. 4ECh. 13.3 - Prob. 5ECh. 13.3 - Prob. 6ECh. 13.3 - Prob. 7ECh. 13.3 - Prob. 8ECh. 13.3 - [BB] Assume that the only short circuits in a...Ch. 13.3 - Prob. 10ECh. 13.3 - 11. Find a best possible feasible relationship...Ch. 13.3 - Prob. 12ECh. 13.3 - Prob. 13ECh. 13.3 - Prob. 14ECh. 13.3 - Prob. 15ECh. 13.3 - [BB] Apply Brookss Theorem (p. 422 ) to find the...Ch. 13 - (a) Show that the graph below is planar by drawing...Ch. 13 - Prob. 2RECh. 13 - Prob. 3RECh. 13 - Prob. 4RECh. 13 - Prob. 5RECh. 13 - Prob. 6RECh. 13 - Prob. 7RECh. 13 - Prob. 8RECh. 13 - Prob. 9RECh. 13 - Prob. 10RECh. 13 - Prob. 11RECh. 13 - Prob. 12RECh. 13 - Prob. 13RECh. 13 - 14. Suppose that in one particular semester there...Ch. 13 - Prob. 15RECh. 13 - 16. Draw the line-of-sight graph associated with...Ch. 13 - Prob. 17RECh. 13 - Prob. 18RECh. 13 - Prob. 19RECh. 13 - A contractor is building a single house for a...Ch. 13 - 23. The Central Newfoundland Hospital Board would...
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