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Discrete Mathematics and its Applications
Found in: Page 804
Discrete Mathematics and its Applications

Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095

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Short Answer

Give at least three examples of how trees are used in modeling.

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Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Definition

Trees are modeling

Trees are commonly used in Chemistry. For example, Saturated Hydrocarbons are often represented as a tree.

Trees are often used to represent the file system on a computer system, where the main directory is the root of the tree and all files/subdirectories in a certain directory are represented as the children of that directory.

Step 2: Trees

Trees are commonly used to describe the structure of a large organization. For example, the structure of the employees and who is the boss of whom; or the structure of the departments of a company and which subdepartments fall under these departments.

Most popular questions for Math Textbooks

a. Describe Kruskal's algorithm and Prim's algorithm for finding minimum spanning trees.

b. Illustrate how Kruskal's algorithm and Prim's algorithm are used to find a minimum spanning tree, using a weighted graph with at least eight vertices and \(15\) edges.

Suppose that \({\bf{e}}\) is an edge in a weighted graph that is incident to a vertex v such that the weight of \({\bf{e}}\) does not exceed the weight of any other edge incident to v. Show that there exists a minimum spanning tree containing this edge.

The eccentricity of a vertex in an unrooted tree is the length of the longest simple path beginning at this vertex. A vertex is called a center if no vertex in the tree has smaller eccentricity than this vertex. In Exercises \({\bf{39--41}}\) find every vertex that is a center in the given tree.

41.

a) Define a full \(m{\bf{ - }}\)ary tree.

b) How many vertices does a full \(m{\bf{ - }}\)ary tree have if it has \({\bf{i}}\) internal vertices\(?\) How many leaves does the tree have?

Draw \({{\bf{B}}_{\bf{k}}}\) for \({\bf{k = 0,1,2,3,4}}\).
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