For Exercises 2730, use a graph to represent the floor

A finite set of points connected by line segments is called a(n) .

A point in a graph is called a(n) .

A line segment in a graph is called a(n) .

An edge that connects a vertex to itself is called a(n) .

A sequence of adjacent vertices and the edges connecting them is called a(n) .

A path that begins and ends with the same vertex is called a(n) .

The number of edges that connect to a vertex is called the of the vertex.

In Exercises 7 and 8, determine whether the graph shown is connected or disconnected.

In Exercises 914, create a graph with the given properties. There are many possible answers for each problem.Four even vertices

In Exercises 914, create a graph with the given properties. There are many possible answers for each problem.Four odd vertices

In Exercises 914, create a graph with the given properties. There are many possible answers for each problem. Two even and two odd vertices

In Exercises 914, create a graph with the given properties. There are many possible answers for each problem. Four odd vertices and one even vertex

In Exercises 914, create a graph with the given properties. There are many possible answers for each problem. Seven vertices and one bridge

In Exercises 9–14, create a graph with the given properties. There are many possible answers for each problem. Seven vertices and two bridges

In Exercises 1520, use the graph below to answer the following questions. E F C D A B.Is A, B, C, D, F, E a path? Explain.

In Exercises 1520, use the graph below to answer the following questions. E F C D A B.Which edge(s) shown on the graph are not included in the following path: A, B, D, F, E, C?

In Exercises 1520, use the graph below to answer the following questions. E F C D A B.On the graph, is it possible to determine a path that begins with vertex A, contains all the edges exactly once, and ends with vertex B? If so, determine one such path.

In Exercises 1520, use the graph below to answer the following questions. E F C D A B.On the graph, is it possible to determine a circuit that includes only four distinct vertices? If so, determine one such circuit.

In Exercises 1520, use the graph below to answer the following questions. E F C D A B.On the graph, can you determine a path that includes all the edges without using any edge twice? If so, determine one such path.

In Exercises 1520, use the graph below to answer the following questions. E F C D A B.On the graph, can you determine a circuit that includes all the vertices without using any vertex (other than the beginning and ending vertex) twice? If so, determine one such circuit.

Modified Konigsberg Bridge In Exercises 21 and 22, suppose that the people of Konigsberg decide to add several bridges to their city. Two such possibilities are shown. Create graphs that would represent the Konigsberg bridge problem with these new bridges.

Modified Knigsberg Bridge Problems In Exercises 21 and 22, suppose that the people of Knigsberg decide to add several bridges to their city. Two such possibilities are shown. Create graphs that would represent the Knigsberg bridge problem with these new bridges.

Other Navy Regions In Exercises 23 and 24, the maps of states that are in other Navy regions (see Example 2 on page 855) are shown. Represent each map as a graph where each vertex represents a state and each edge represents a common border between the states. Use the state abbreviations to label the vertices of the graph.

Other Navy Regions In Exercises 23 and 24, the maps of states that are in other Navy regions (see Example 2 on page 855) are shown. Represent each map as a graph where each vertex represents a state and each edge represents a common border between the states. Use the state abbreviations to label the vertices of the graph.

Central America The map below shows the countries of Belize (B ), Costa Rica (C ), El Salvador (E ), Guatemala (G ), Honduras (H ), Nicaragua (N ), and Panama (P). Represent the map as a graph where each vertex represents a country and each edge represents a common border between the countries. Use the letters indicated in parentheses to label the vertices. Guatemala Belize Honduras Nicaragua Costa Rica Panama El Salvador

Northern Africa The map below shows the countries of Algeria (A ), Egypt (E ), Libya (L ), Morocco (M ), Sudan (S ), Tunisia (T), and Western Sahara (W ). Represent the map as a graph where each vertex represents a country and each edge represents a common border between the countries. Use the letters indicated in parentheses to label the vertices. Egypt Morocco Algeria Sudan Libya Western Sahara Tunisia

For Exercises 27-30, use a graph to represent the floor plan shown. In each graph, use the letter O to represent the outside of the building. See Example 3, page 857. Floor Plan The drawing below shows the first-floor plan of the Aloha model home offered by the Kim Ghiselin Family Construction Company of Woonsocket, Rhode Island. Place vertex O near the top of the graph.

For Exercises 2730, use a graph to represent the floor plan shown. In each graph, use the letter O to represent the outside of the building. See Example 3, page 857.Floor Plan The drawing below shows the floor plan of the Sun Valley model home offered by Wubben Builders of Pocatello, Idaho. Place vertex O near the bottom of the graph. Master Bedroom Guest Bedroom Gallery Outside Office Bathroom Living Room Kitchen/ Dining Room

For Exercises 27–30, use a graph to represent the floor plan shown. In each graph, use the letter O to represent the outside of the building. See Example 3, page 857. Floor Plan The drawing below shows the floor plan of the first floor of the Oleander model home offered by Nisely Builders of Albuquerque, New Mexico. Place vertex O near the bottom of the graph.

For Exercises 2730, use a graph to represent the floor plan shown. In each graph, use the letter O to represent the outside of the building. See Example 3, page 857.Floor Plan The drawing below shows the floor plan of the Bougainvillea model home offered by Alstrom Builders of Waco, Texas. Place vertex O near the bottom of the graph. First Bedroom Recreation Room Den Master Bedroom Kitchen Living Room Second Bedroom Garage Dining Room Hall Guest Bathroom Bathroom Outside

Representing a Neighborhood The map of the Tree Tops subdivision in Prince George County, Virginia, is shown below. Use a graph to represent the streets in this subdivision. Use letters to label the vertices. Lake Lake Park Lake Lake Walnut St. Pine St. Elm St. Oak St. Willow St. Fir St. Maple Cir

Representing a Neighborhood The map of the Crescent Lakes subdivision in Essex County, Maryland, is shown below. Use a graph to represent the streets in this subdivision. Use letters to label the vertices.

In Exercises 3336, determine whether the graph shown is connected or disconnected.

In Exercises 3336, determine whether the graph shown is connected or disconnected.

In Exercises 3336, determine whether the graph shown is connected or disconnected.

In Exercises 3336, determine whether the graph shown is connected or disconnected.

In Exercises 37 40, a connected graph is shown. Identify any bridges in each graph.

In Exercises 37 40, a connected graph is shown. Identify any bridges in each graph.

In Exercises 37 40, a connected graph is shown. Identify any bridges in each graph.

In Exercises 37 40, a connected graph is shown. Identify any bridges in each graph.

Poll your entire class to determine which students knew each other prior to taking this course. Draw a graph that shows this relationship.

Attempt to draw a graph that has an odd number of odd vertices. What conclusion can you draw from this exercise?

Draw four different graphs and then for each graph: a) determine the degree of each vertex.

Facebook Friends Read the Recreational Mathematics box on page 855. Belinda, Dennis, Jeff, Kristie, Lucy, and Mike are all on Facebook. The following pairs of people are friends: Belinda and Dennis, Belinda and Kristie, Belinda and Lucy, Dennis and Kristie, Dennis and Lucy, Dennis and Mike, Jeff and Lucy, Kristie and Lucy, and Kristie and Mike. Represent the friendships with a graph.

Use a graph to represent a) the floor plan of your home. b) the streets in your neighborhood within \(\frac{1}{2}\) mile from your home in all directions.

Choose a continent other than North America or Australia and create a graph showing the common boundaries between countries. Be sure to use a current map.