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mathematics
survey of mathematics

Questions and Answers of Survey of Mathematics

Is it possible to have a path that begins at vertex A, includes all edges exactly once, and ends at vertex B?Use the following graph. A B C• Н
Determine a path that passes through each edge exactly one time.Use the following graph. A B C• Н
Create a graph with four even vertices and two loops.Create a graph with the given properties.
Create a graph with four even vertices, two odd vertices, a bridge, and a loop.Create a graph with the given properties.
The state of Illinois is applying for a grant to connect several metropolitan areas of the state with a light-rail transport system. The cities involved are Urbana, Chicago, Peoria, Rockford, and
The Missouri Park and Recreation Association would like to build a recreation trail for biking and hiking that connects the cities of Jefferson City, Kansas City, Springfield, St. Joseph, and St.
The Ohio Recreation Council is interested in creating bicycle trails connecting the following cities: Akron, Cleveland, Dayton, Toledo, and Youngstown. The distances, in miles, between these cities
The Darlington County, South Carolina, tourism office wishes to build a horse trail that connects the towns of Darlington, Hartsville, Lamar, and Society Hill. The distances, in miles, between these
Five of the campuses in the University of Texas system would like to establish a high-speed telephone and data network between the campuses. The campuses are located in the following cities:
Several communities in eastern Pennsylvania wish to establish a commuter rail train system between the cities shown in the map below (distances are in miles).(a) Use Kruskal’s algorithm to
Joe is creating a modern art sculpture that needs to have electricity available at five different sites. The figure below shows the items included in the sculpture. The distances shown are in
Ruth wishes to install an irrigation system to water her five flower gardens. The distances in feet between her gardens are shown in the figure below.(a) Represent this information with a weighted
Determine the minimum-cost spanning trees for the given graph. B 13 10 66 97 21 D 12 5
Determine the minimum-cost spanning trees for the given graph. A 67 B D 73 96 23 42 12 37 38 31 F 61 Н 2.
Determine the minimum-cost spanning trees for the given graph. 12 12 B D 5 2 5/ 10 1 I E 9 F 3 4 4 H 11
Determine the minimum-cost spanning trees for the given graph. B 13 17 20 15 14 18 E D 16
Determine the minimum-cost spanning trees for the given graph. A 100 B 85 95 90, 75 80 70 E 65 F
Determine the minimum-cost spanning trees for the given graph. A 3 36 B 14 21 D Н 1 15 49 31 27
Determine the minimum-cost spanning trees for the given graph. 16 19 5 4, 8. B. 3.
Determine the minimum-cost spanning trees for the given graph. B 5 20 10 (15 30 25 35
Determine two different spanning trees for the given graph. There are many possible answers. B G Н
Determine two different spanning trees for the given graph. There are many possible answers. B D G Н
Determine two different spanning trees for the given graph. There are many possible answers. A B. D« H.
Determine two different spanning trees for the given graph. There are many possible answers. B A OD Н
Determine two different spanning trees for the given graph. There are many possible answers. B De
Determine two different spanning trees for the given graph. There are many possible answers. в с B A D
Use a tree to show the following supervisory relationships at Halford College. President Downing supervises three division directors: Hill, Tipton, and Davis. Hill supervises two department chairs:
Use a tree to show the following supervisory relationships at DTX Industries. Kroger is president and has three vice presidents: Dorfman, Blutar-sky, and Hoover. Dorfman has three managers: Stratton,
Use a tree to show the parent–child relation-ships in the following family. Joe has two children: Allan and Rosemary. Allan has three children: Christopher, Donetta, and AJ. Rosemary has three
Use a tree to show the parent–child relation-ships in the following family. Angela has two sons, Eli and Connor. Eli has four children: Jason, Max, Gabriella, and Tony. Connor has three children:
Fill in the blanks with an appropriate word, phrase, or symbol(s).To determine the minimum-cost spanning tree for a weighted graph, we can use ___________ algorithm.
Fill in the blanks with an appropriate word, phrase, or symbol(s).The least expensive spanning tree of all spanning trees under consideration is called the ________ spanning tree.
Fill in the blanks with an appropriate word, phrase, or symbol(s).A tree that is created from another graph by removing edges while still maintaining a path to each vertex is called a(n) __________
Fill in the blanks with an appropriate word, phrase, or symbol(s).A tree does not have any Euler or Hamilton ___________ .
Fill in the blanks with an appropriate word, phrase, or symbol(s).If you remove any edge in a tree, it creates a(n) _________ graph.
Fill in the blanks with an appropriate word, phrase, or symbol(s).A connected graph in which each edge is a bridge is called a(n) __________ .
In 1857, William Rowan Hamilton invented the game called the Icosian Game. The game consisted of a round board with 20 holes and 20 numbered pegs. On the surface of the board was a pattern similar to
The following tasks are intended to help you understand the formula for finding the number of unique Hamilton circuits in a complete graph. (a) Draw a complete graph with three vertices labeled
Altay lives in Boston, Massachusetts, and works for Ocean Spray Cranberries, Inc. Altay wishes to visit cranberry farms in the following locations: Madison, Wisconsin; Princeton, New Jersey; Salem,
Jim, the chief executive officer of Bass Pro Shops, is at his office in Springfield, Missouri, and is considering adding new stores in the following locations: Bismarck, North Dakota; Carson City,
Jasmine lives in Elko, Nevada (E), and is planning a trip to see the following basketball teams play on their home courts: Utah Jazz (J), Sacramento Kings (K), Portland Trailblazers (T), and Golden
Laurice works for FedEx and is in her office (O). She has packages to deliver to the following families: Moller (M), Ransford (R), Seifert (S), and Warren (W). The approximate distances among these
The State College of Florida Brain Bowl team is in Bradenton, Florida (B), and is planning a trip over spring break. The team plans to visit Washington, DC (W); Montgomery, AL (M); and Savannah, GA
The Ackermans live in Tunkhannock, Pennsylvania (T), and are planning their summer vacation. They wish to visit the following national parks: Acadia (A), Cuyahoga Valley (C), and Great Smoky
Christina is searching for a new job. She lives in Shreveport, Louisiana, and has interviews in Barrow, Alaska; Tucson, Arizona; and Rochester, New York. The costs of the one-way flights between
Mary needs to run errands on the campus of Clarke University. She is in her office and needs to go to the duplicating center, student center, and library. She estimates the walking distances as
Dale is a milk truck driver for Swiss Valley Farms Cooperative in eastern Iowa. Dale has to start at the processing plant and pick up milk on 10 different farms. In how many ways can Dale visit each
Sally lives in Nashville, Tennessee, and works for the Department of Transportation. She wishes to inspect weigh stations in the following Tennessee cities: Caruthersville, Clarksville, Cleveland,
Craig, the president of Culver’s Restaurants, is at his home in Prairie du Sac, WI, and wishes to investigate locations for a new restaurant in the following cities: Robinson, IL; Erie, PA;
Nick is a high school student who lives in Bakersfield, CA, and he wishes to visit colleges in the following cities: St. Cloud, MN; Valparaiso, IN; Lindonville, VT; Asheville, NC; and Norman, OK. In
Draw a complete graph with five vertices.
Draw a complete graph with four vertices.
Determine two different Hamilton circuits in each of the following graphs. B De E F Н
Determine two different Hamilton circuits in each of the following graphs. De Н
Determine two different Hamilton circuits in each of the following graphs. A B F G Н Гл K L
Determine two different Hamilton circuits in each of the following graphs. A B F G Н
Determine two different Hamilton paths in each of the following graphs. A B De G Н I
Determine two different Hamilton paths in each of the following graphs. F• De
Determine two different Hamilton paths in each of the following graphs. Ce Н
Determine two different Hamilton paths in each of the following graphs. D B G Н
Determine two different Hamilton paths in each of the following graphs. D в
Determine two different Hamilton paths in each of the following graphs. в B D Н
Fill in the blanks with an appropriate word, phrase, or symbol(s).The method discussed in this section that will determine an approximate solution to a traveling salesman problem is the nearest
Fill in the blanks with an appropriate word, phrase, or symbol(s).The method discussed in this section that will determine the optimal solution to a traveling salesman problem is the brute ________
Fill in the blanks with an appropriate word, phrase, or symbol(s).In a traveling salesman problem, the Hamilton circuit with the lowest associated cost or shortest distance is called the ___________
Fill in the blanks with an appropriate word, phrase, or symbol(s).Every complete graph has a Hamilton circuit but not necessarily a(n)________ circuit.
Fill in the blanks with an appropriate word, phrase, or symbol(s).A graph that has exactly one edge between each pair of vertices is called a(n) ________ graph
Fill in the blanks with an appropriate word, phrase, or symbol(s).A path that begins and ends at the same vertex and passes through all other vertices of a graph exactly one time is called a(n)
Fill in the blanks with an appropriate word, phrase, or symbol(s).A graph that has numbers along the edges to indicate cost or distance is called a(n) ________ graph.
Fill in the blanks with an appropriate word, phrase, or symbol(s).Problems that generally involve seeking the least expensive or shortest way to travel among several locations are called traveling
(a) Draw a graph with one vertex that has both an Euler path and an Euler circuit.(b) Draw a graph with two vertices that has an Euler path but no Euler circuit. (c) Draw a graph with two
Attempt to draw a graph with an Euler circuit that has a bridge. What conclusion can you develop from this exercise?
Consider a map of the contiguous United States. Imagine a graph with 48 vertices in which each vertex represents one of the contiguous states. Each edge would represent a common border between
Imagine a very large connected graph that has 200 odd vertices and 200 even vertices.(a) Does an Euler path exist for this graph? Explain.(b) Does an Euler circuit exist for this graph? Explain.
Imagine a very large connected graph that has 400 odd vertices and no even vertices.(a) Does an Euler path exist for this graph? Explain.(b) Does an Euler circuit exist for this graph? Explain.
Imagine a very large connected graph that has two odd vertices and 398 even vertices.(a) Does an Euler path exist for this graph? Explain.(b) Does an Euler circuit exist for this graph? Explain.
Imagine a very large connected graph that has 400 even vertices and no odd vertices.(a) Does an Euler path exist for this graph? Explain. (b) Does an Euler circuit exist for this graph? Explain.
Determine an Euler circuit for the Country Oaks crime stopper group that begins with vertex J followed by vertex F.
Determine an Euler circuit for the Country Oaks crime stopper group that begins with vertex J followed by vertex G.
Determine an Euler circuit for the Country Oaks crime stopper group that begins with vertex B followed by vertex E.
Determine an Euler circuit for the Country Oaks crime stopper group that begins with vertex B followed by vertex A.
Determine an Euler path for the Phenomenal Phitness Gym that begins in locker room (vertex) A.
Determine an Euler path through the states in the Navy Region Southwest that begins with the state of Utah.
Use Fleury’s algorithm to determine an Euler circuit. A B D Н G K
Use Fleury’s algorithm to determine an Euler circuit. B Н
Use Fleury’s algorithm to determine an Euler circuit. A B D E
Use Fleury’s algorithm to determine an Euler circuit. A Be Н
Use Fleury’s algorithm to determine an Euler circuit. B Н
Use Fleury’s algorithm to determine an Euler circuit. B Н
Use Fleury’s algorithm to determine an Euler path. B D C. н N к
Use Fleury’s algorithm to determine an Euler path. De G Н
Use Fleury’s algorithm to determine an Euler path. De OF Н G
Use Fleury’s algorithm to determine an Euler path. A B c D E
(a) Determine whether the residents in each subdivision will be able to establish a path through their communities so that each street block is walked exactly one time.(b) If yes, where would the
(a) Determine whether the residents in each subdivision will be able to establish a path through their communities so that each street block is walked exactly one time.(b) If yes, where would the
Recall Joe from who runs a gym-cleaning service. Joe is also responsible for locking the doors of four other gyms. (a) Represent each floor plan as a graph. Use the letters shown to label the
Recall Joe from who runs a gym-cleaning service. Joe is also responsible for locking the doors of four other gyms. (a) Represent each floor plan as a graph. Use the letters shown to label the
Recall Joe from who runs a gym-cleaning service. Joe is also responsible for locking the doors of four other gyms. (a) Represent each floor plan as a graph. Use the letters shown to label the
Recall Joe from who runs a gym-cleaning service. Joe is also responsible for locking the doors of four other gyms. (a) Represent each floor plan as a graph. Use the letters shown to label the
Use each map shown.(a) Represent the map as a graph. Use the letter indicated in parentheses to label vertices of the graph. (b) Determine (state yes or no) whether the graph in part (a) has an

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