(a) To define: A tree.

Question

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Answer 1

Question

Chapter 11, Problem 1RQ

To determine

(a)

To define:

A tree.

Expert Solution

Explanation of Solution

Definition: A tree is a connected undirected graph with no simple circuits. Because a tree cannot have a simple circuit, a tree cannot contain multiple edges or loops. Therefore any tree must be a simple graph.

An undirected graph is a tree if and only if there is a unique simple path between any two of its vertices.

Example:

DISCRETE MATHEMATICS+ITS APPL. (LL)-W/A, Chapter 11, Problem 1RQ , additional homework tip 1

To determine

(b)

To define:

A forest.

Expert Solution

Explanation of Solution

Definition: A forest is an undirected graph, all of whose connected components are trees.

i.e. the graph consists of a disjoint union of trees.

A forest is a disjoint union of trees, or equivalently anacyclic graph that is not necessarily connected.

Example:

DISCRETE MATHEMATICS+ITS APPL. (LL)-W/A, Chapter 11, Problem 1RQ , additional homework tip 2

An empty graph, a single tree and the discrete graph on a set of vertices are examples of forest tree.

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Answer 2

Question

Chapter 11, Problem 1RQ

To determine

(a)

To define:

A tree.

Expert Solution

Explanation of Solution

Definition: A tree is a connected undirected graph with no simple circuits. Because a tree cannot have a simple circuit, a tree cannot contain multiple edges or loops. Therefore any tree must be a simple graph.

An undirected graph is a tree if and only if there is a unique simple path between any two of its vertices.

Example:

DISCRETE MATHEMATICS+ITS APPL. (LL)-W/A, Chapter 11, Problem 1RQ , additional homework tip 1

To determine

(b)

To define:

A forest.

Expert Solution

Explanation of Solution

Definition: A forest is an undirected graph, all of whose connected components are trees.

i.e. the graph consists of a disjoint union of trees.

A forest is a disjoint union of trees, or equivalently anacyclic graph that is not necessarily connected.

Example:

DISCRETE MATHEMATICS+ITS APPL. (LL)-W/A, Chapter 11, Problem 1RQ , additional homework tip 2

An empty graph, a single tree and the discrete graph on a set of vertices are examples of forest tree.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Chapter 11, Problem 1RQ

To determine

(a)

To define:

A tree.

Expert Solution

Explanation of Solution

Definition: A tree is a connected undirected graph with no simple circuits. Because a tree cannot have a simple circuit, a tree cannot contain multiple edges or loops. Therefore any tree must be a simple graph.

An undirected graph is a tree if and only if there is a unique simple path between any two of its vertices.

Example:

DISCRETE MATHEMATICS+ITS APPL. (LL)-W/A, Chapter 11, Problem 1RQ , additional homework tip 1

To determine

(b)

To define:

A forest.

Expert Solution

Explanation of Solution

Definition: A forest is an undirected graph, all of whose connected components are trees.

i.e. the graph consists of a disjoint union of trees.

A forest is a disjoint union of trees, or equivalently anacyclic graph that is not necessarily connected.

Example:

DISCRETE MATHEMATICS+ITS APPL. (LL)-W/A, Chapter 11, Problem 1RQ , additional homework tip 2

An empty graph, a single tree and the discrete graph on a set of vertices are examples of forest tree.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 11, Problem 1RQ

To determine

(a)

To define:

A tree.

Expert Solution

Explanation of Solution

Definition: A tree is a connected undirected graph with no simple circuits. Because a tree cannot have a simple circuit, a tree cannot contain multiple edges or loops. Therefore any tree must be a simple graph.

An undirected graph is a tree if and only if there is a unique simple path between any two of its vertices.

Example:

DISCRETE MATHEMATICS+ITS APPL. (LL)-W/A, Chapter 11, Problem 1RQ , additional homework tip 1

To determine

(b)

To define:

A forest.

Expert Solution

Explanation of Solution

Definition: A forest is an undirected graph, all of whose connected components are trees.

i.e. the graph consists of a disjoint union of trees.

A forest is a disjoint union of trees, or equivalently anacyclic graph that is not necessarily connected.

Example:

DISCRETE MATHEMATICS+ITS APPL. (LL)-W/A, Chapter 11, Problem 1RQ , additional homework tip 2

An empty graph, a single tree and the discrete graph on a set of vertices are examples of forest tree.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 11, Problem 1RQ

To determine

(a)

To define:

A tree.

Expert Solution

Explanation of Solution

Definition: A tree is a connected undirected graph with no simple circuits. Because a tree cannot have a simple circuit, a tree cannot contain multiple edges or loops. Therefore any tree must be a simple graph.

An undirected graph is a tree if and only if there is a unique simple path between any two of its vertices.

Example:

DISCRETE MATHEMATICS+ITS APPL. (LL)-W/A, Chapter 11, Problem 1RQ , additional homework tip 1

To determine

(b)

To define:

A forest.

Expert Solution

Explanation of Solution

Definition: A forest is an undirected graph, all of whose connected components are trees.

i.e. the graph consists of a disjoint union of trees.

A forest is a disjoint union of trees, or equivalently anacyclic graph that is not necessarily connected.

Example:

DISCRETE MATHEMATICS+ITS APPL. (LL)-W/A, Chapter 11, Problem 1RQ , additional homework tip 2

An empty graph, a single tree and the discrete graph on a set of vertices are examples of forest tree.

Answer 6

Chapter 11, Problem 1RQ

To determine

(a)

To define:

A tree.

Expert Solution

Explanation of Solution

Definition: A tree is a connected undirected graph with no simple circuits. Because a tree cannot have a simple circuit, a tree cannot contain multiple edges or loops. Therefore any tree must be a simple graph.

An undirected graph is a tree if and only if there is a unique simple path between any two of its vertices.

Example:

DISCRETE MATHEMATICS+ITS APPL. (LL)-W/A, Chapter 11, Problem 1RQ , additional homework tip 1

Answer 7

Chapter 11, Problem 1RQ

To determine

(a)

To define:

A tree.

Answer 8

Expert Solution

Explanation of Solution

Definition: A tree is a connected undirected graph with no simple circuits. Because a tree cannot have a simple circuit, a tree cannot contain multiple edges or loops. Therefore any tree must be a simple graph.

An undirected graph is a tree if and only if there is a unique simple path between any two of its vertices.

Example:

DISCRETE MATHEMATICS+ITS APPL. (LL)-W/A, Chapter 11, Problem 1RQ , additional homework tip 1

Answer 9

Expert Solution

Answer 10

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

(b)

To define:

A forest.

Expert Solution

Explanation of Solution

Definition: A forest is an undirected graph, all of whose connected components are trees.

i.e. the graph consists of a disjoint union of trees.

A forest is a disjoint union of trees, or equivalently anacyclic graph that is not necessarily connected.

Example:

DISCRETE MATHEMATICS+ITS APPL. (LL)-W/A, Chapter 11, Problem 1RQ , additional homework tip 2

An empty graph, a single tree and the discrete graph on a set of vertices are examples of forest tree.

Answer 13

To determine

(b)

To define:

A forest.

Answer 14

Expert Solution

Explanation of Solution

Definition: A forest is an undirected graph, all of whose connected components are trees.

i.e. the graph consists of a disjoint union of trees.

A forest is a disjoint union of trees, or equivalently anacyclic graph that is not necessarily connected.

Example:

DISCRETE MATHEMATICS+ITS APPL. (LL)-W/A, Chapter 11, Problem 1RQ , additional homework tip 2

An empty graph, a single tree and the discrete graph on a set of vertices are examples of forest tree.

Answer 15

Expert Solution

Answer 16

Expert Solution

Answer 17

Expert Solution

Answer 18

Ch. 11.1 - Prob. 1E Ch. 11.1 - Vhich of these graphs are trees?Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E

(a) To define: A tree.

(a) To define: A tree.

Explanation of Solution

(b) To define: A forest.

Explanation of Solution

Want to see more full solutions like this?

Chapter 11 Solutions

(a)

To define:

A tree.

(b)

To define:

A forest.