a) Define a simple graph, a multigraph, a pseudograph, a directed graph, and a directed multigraph. b) Use an example to show how each of the types of graph in part (a) can be used in modeling. For example, explain how to model different aspects of a computer network or airline routes.

Question

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Answer 1

Textbook Question

Chapter 10, Problem 1RQ

a) Define a simple graph, a multigraph, a pseudograph, a directed graph, and a directed multigraph.

b) Use an example to show how each of the types of graph in part (a) can be used in modeling. For example, explain how to model different aspects of a computer network or airline routes.

Expert Solution

To determine

(a)

Define a simple graph, a multigraph, a pseudograph,a directed graph, and a directed multigraph.

Explanation of Solution

Calculation:

Simple graph: an undirected graph with no multiple edge or loops.

Multipgraph: an undirected graph that may contain multiple edges but no loops.

Pseudograph: an undirected graph that may contain multiple edges and loops.

Directed graph: a set of vertices together with a set of directed edges each of which is associated with an ordered pair of vertices.

Directed multigraph: a graph with directed edges that may contain multiple directed edges.

Expert Solution

To determine

(b)

Use an example to showhoweach of the types of graphin part (a) can be used in modeling.

Explanation of Solution

Calculation:

Simple graph: a friends network (i.e. Facebook, Twitter)

Multigraph: bridges between islands (i.e. the bridges of Knigserg); since youmay have multiple bridges 2 islands but not a single bridge to the same island.

Pseudograph: websites and their hyperlinks, where a website with a hyperlink to itself would be a loop.

For the following graph applications we take edge as distances and the vertices as places with the lines being links between them:

Directed graph: an airline route.

Directed multigraph: a road network.

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Answer 2

Textbook Question

Chapter 10, Problem 1RQ

a) Define a simple graph, a multigraph, a pseudograph, a directed graph, and a directed multigraph.

b) Use an example to show how each of the types of graph in part (a) can be used in modeling. For example, explain how to model different aspects of a computer network or airline routes.

Expert Solution

To determine

(a)

Define a simple graph, a multigraph, a pseudograph,a directed graph, and a directed multigraph.

Explanation of Solution

Calculation:

Simple graph: an undirected graph with no multiple edge or loops.

Multipgraph: an undirected graph that may contain multiple edges but no loops.

Pseudograph: an undirected graph that may contain multiple edges and loops.

Directed graph: a set of vertices together with a set of directed edges each of which is associated with an ordered pair of vertices.

Directed multigraph: a graph with directed edges that may contain multiple directed edges.

Expert Solution

To determine

(b)

Use an example to showhoweach of the types of graphin part (a) can be used in modeling.

Explanation of Solution

Calculation:

Simple graph: a friends network (i.e. Facebook, Twitter)

Multigraph: bridges between islands (i.e. the bridges of Knigserg); since youmay have multiple bridges 2 islands but not a single bridge to the same island.

Pseudograph: websites and their hyperlinks, where a website with a hyperlink to itself would be a loop.

For the following graph applications we take edge as distances and the vertices as places with the lines being links between them:

Directed graph: an airline route.

Directed multigraph: a road network.

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Answer 3

Textbook Question

Chapter 10, Problem 1RQ

a) Define a simple graph, a multigraph, a pseudograph, a directed graph, and a directed multigraph.

b) Use an example to show how each of the types of graph in part (a) can be used in modeling. For example, explain how to model different aspects of a computer network or airline routes.

Expert Solution

To determine

(a)

Define a simple graph, a multigraph, a pseudograph,a directed graph, and a directed multigraph.

Explanation of Solution

Calculation:

Simple graph: an undirected graph with no multiple edge or loops.

Multipgraph: an undirected graph that may contain multiple edges but no loops.

Pseudograph: an undirected graph that may contain multiple edges and loops.

Directed graph: a set of vertices together with a set of directed edges each of which is associated with an ordered pair of vertices.

Directed multigraph: a graph with directed edges that may contain multiple directed edges.

Expert Solution

To determine

(b)

Use an example to showhoweach of the types of graphin part (a) can be used in modeling.

Explanation of Solution

Calculation:

Simple graph: a friends network (i.e. Facebook, Twitter)

Multigraph: bridges between islands (i.e. the bridges of Knigserg); since youmay have multiple bridges 2 islands but not a single bridge to the same island.

Pseudograph: websites and their hyperlinks, where a website with a hyperlink to itself would be a loop.

For the following graph applications we take edge as distances and the vertices as places with the lines being links between them:

Directed graph: an airline route.

Directed multigraph: a road network.

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Answer 4

Textbook Question

Chapter 10, Problem 1RQ

a) Define a simple graph, a multigraph, a pseudograph, a directed graph, and a directed multigraph.

b) Use an example to show how each of the types of graph in part (a) can be used in modeling. For example, explain how to model different aspects of a computer network or airline routes.

Expert Solution

To determine

(a)

Define a simple graph, a multigraph, a pseudograph,a directed graph, and a directed multigraph.

Explanation of Solution

Calculation:

Simple graph: an undirected graph with no multiple edge or loops.

Multipgraph: an undirected graph that may contain multiple edges but no loops.

Pseudograph: an undirected graph that may contain multiple edges and loops.

Directed graph: a set of vertices together with a set of directed edges each of which is associated with an ordered pair of vertices.

Directed multigraph: a graph with directed edges that may contain multiple directed edges.

Expert Solution

To determine

(b)

Use an example to showhoweach of the types of graphin part (a) can be used in modeling.

Explanation of Solution

Calculation:

Simple graph: a friends network (i.e. Facebook, Twitter)

Multigraph: bridges between islands (i.e. the bridges of Knigserg); since youmay have multiple bridges 2 islands but not a single bridge to the same island.

Pseudograph: websites and their hyperlinks, where a website with a hyperlink to itself would be a loop.

For the following graph applications we take edge as distances and the vertices as places with the lines being links between them:

Directed graph: an airline route.

Directed multigraph: a road network.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution

To determine

(a)

Define a simple graph, a multigraph, a pseudograph,a directed graph, and a directed multigraph.

Explanation of Solution

Calculation:

Simple graph: an undirected graph with no multiple edge or loops.

Multipgraph: an undirected graph that may contain multiple edges but no loops.

Pseudograph: an undirected graph that may contain multiple edges and loops.

Directed graph: a set of vertices together with a set of directed edges each of which is associated with an ordered pair of vertices.

Directed multigraph: a graph with directed edges that may contain multiple directed edges.

Expert Solution

To determine

(b)

Use an example to showhoweach of the types of graphin part (a) can be used in modeling.

Explanation of Solution

Calculation:

Simple graph: a friends network (i.e. Facebook, Twitter)

Multigraph: bridges between islands (i.e. the bridges of Knigserg); since youmay have multiple bridges 2 islands but not a single bridge to the same island.

Pseudograph: websites and their hyperlinks, where a website with a hyperlink to itself would be a loop.

For the following graph applications we take edge as distances and the vertices as places with the lines being links between them:

Directed graph: an airline route.

Directed multigraph: a road network.

Answer 8

Expert Solution

To determine

(a)

Define a simple graph, a multigraph, a pseudograph,a directed graph, and a directed multigraph.

Explanation of Solution

Calculation:

Simple graph: an undirected graph with no multiple edge or loops.

Multipgraph: an undirected graph that may contain multiple edges but no loops.

Pseudograph: an undirected graph that may contain multiple edges and loops.

Directed graph: a set of vertices together with a set of directed edges each of which is associated with an ordered pair of vertices.

Directed multigraph: a graph with directed edges that may contain multiple directed edges.

Answer 9

Expert Solution

Answer 10

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

(a)

Define a simple graph, a multigraph, a pseudograph,a directed graph, and a directed multigraph.

Answer 13

Explanation of Solution

Calculation:

Simple graph: an undirected graph with no multiple edge or loops.

Multipgraph: an undirected graph that may contain multiple edges but no loops.

Pseudograph: an undirected graph that may contain multiple edges and loops.

Directed graph: a set of vertices together with a set of directed edges each of which is associated with an ordered pair of vertices.

Directed multigraph: a graph with directed edges that may contain multiple directed edges.

Answer 14

Expert Solution

To determine

(b)

Use an example to showhoweach of the types of graphin part (a) can be used in modeling.

Explanation of Solution

Calculation:

Simple graph: a friends network (i.e. Facebook, Twitter)

Multigraph: bridges between islands (i.e. the bridges of Knigserg); since youmay have multiple bridges 2 islands but not a single bridge to the same island.

Pseudograph: websites and their hyperlinks, where a website with a hyperlink to itself would be a loop.

For the following graph applications we take edge as distances and the vertices as places with the lines being links between them:

Directed graph: an airline route.

Directed multigraph: a road network.

Answer 15

Expert Solution

Answer 16

Expert Solution

Answer 17

Expert Solution

Answer 18

To determine

(b)

Use an example to showhoweach of the types of graphin part (a) can be used in modeling.

Answer 19

Explanation of Solution

Calculation:

Simple graph: a friends network (i.e. Facebook, Twitter)

Multigraph: bridges between islands (i.e. the bridges of Knigserg); since youmay have multiple bridges 2 islands but not a single bridge to the same island.

Pseudograph: websites and their hyperlinks, where a website with a hyperlink to itself would be a loop.

For the following graph applications we take edge as distances and the vertices as places with the lines being links between them:

Directed graph: an airline route.

Directed multigraph: a road network.